Fractions and Decimals — Free Pre-Algebra Review Games.

Find common denominator 4: 2/4 + 1/4 = 3/4.

0.75 = 75/100 = 3/4 after dividing by 25.

Divide 3 by 5: 3/5 = 0.6.

2 * 3 + 1 = 7, so 2 1/3 = 7/3.

2/3 = 10/15 and 3/5 = 9/15, so 2/3 is larger.

Multiply numerators and denominators: 6/12 = 1/2.

Dividing by a fraction means multiplying by its reciprocal: 3/4 * 2/1 = 6/4 = 3/2.

0.125 = 125/1000 = 1/8 after simplifying.

Convert 1/3 to 2/6, then 5/6 - 2/6 = 3/6 = 1/2.

Line up decimals and add: 1.50 + 2.75 = 4.25.

Convert to eighths: 22/8 - 13/8 = 9/8 = 1 1/8.

5/11 = 0.4545... which rounds to 0.45.

1/3 = 0.333, 3/8 = 0.375, 0.4 = 0.400. Order: 1/3, 3/8, 0.4.

Square both numerator and denominator: (2/3)^2 = 4/9.

Convert to improper: 7/2 * 12/5 = 84/10 = 42/5 = 8 2/5.

To add fractions with different denominators, convert to a common denominator: \(\frac{1}{3} = \frac{2}{6}\), so \(\frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}\). The choice \(\frac{2}{9}\) is wrong because it comes from incorrectly adding numerators and denominators separately instead of finding a common denominator. Always find a common denominator before adding or subtracting fractions.

\(0.5\) means five tenths, or \(\frac{5}{10}\), which simplifies to \(\frac{1}{2}\) by dividing numerator and denominator by 5. The choice \(\frac{5}{10}\) is technically equal but not in simplest form, since both terms share a common factor of 5. Always reduce a fraction to lowest terms by dividing by the greatest common factor.

Dividing 3 by 4 gives \(0.75\), since \(\frac{3}{4}\) means 3 divided into 4 equal parts. The choice \(0.34\) is wrong because it simply rearranges the digits of the fraction rather than performing the division. To convert a fraction to a decimal, always divide the numerator by the denominator.

To convert a mixed number, multiply the whole number by the denominator and add the numerator: \(4 \times 2 + 1 = 9\), giving \(\frac{9}{2}\). The choice \(\frac{5}{2}\) is wrong because it only adds the whole number and numerator without multiplying by the denominator first. Remember the rule: multiply, then add, keeping the same denominator.

When the numerator is the same, a larger denominator means the fraction is divided into more, smaller pieces, so \(\frac{1}{6}\) is smaller than \(\frac{1}{4}\). The choice \(\frac{1}{4}\) is wrong because it represents dividing a whole into fewer, larger pieces, making each piece bigger. When comparing unit fractions, the fraction with the larger denominator is always smaller.

Dividing 2 by 5 gives \(0.4\), since \(\frac{2}{5} = \frac{4}{10} = 0.4\). The choice \(0.25\) is wrong because that value equals \(\frac{1}{4}\), a different fraction entirely. To convert any fraction to a decimal, divide the numerator by the denominator.

Since the denominators are already the same, add the numerators: \(5 + 1 = 6\), giving \(\frac{6}{8}\), which simplifies to \(\frac{3}{4}\). The choice \(\frac{6}{16}\) is wrong because it incorrectly adds the denominators together instead of keeping the common denominator unchanged. When adding fractions with like denominators, only add the numerators and simplify the result.

A fraction with a denominator of 10 converts directly to a decimal by placing the numerator in the tenths place, giving \(0.7\). The choice \(0.07\) is wrong because it places the digit in the hundredths place instead of the tenths place. Fractions with denominators of 10, 100, or 1000 convert easily by matching place value.

Multiply the whole number by the denominator and add the numerator: \(1 \times 4 + 3 = 7\), so the improper fraction is \(\frac{7}{4}\). The choice \(\frac{4}{3}\) is wrong because it swaps the numerator and denominator instead of following the conversion rule. Always multiply the whole number by the denominator first, then add the numerator, keeping the original denominator.

Dividing 1 by 8 gives \(0.125\), since \(\frac{1}{8} = \frac{125}{1000}\). The choice \(0.18\) is wrong because it simply combines the digits 1 and 8 from the fraction rather than performing actual division. Always perform long division of numerator by denominator to find the exact decimal value.

Convert \(\frac{1}{4}\) to eighths: \(\frac{1}{4} = \frac{2}{8}\), so \(\frac{3}{8} + \frac{2}{8} = \frac{5}{8}\). The choice \(\frac{4}{12}\) is wrong because it comes from adding numerators and denominators directly instead of finding a common denominator first. Always rewrite fractions with a shared denominator before combining them.

Since the denominators match, subtract the numerators directly: \(7 - 2 = 5\), giving \(\frac{5}{9}\). The choice \(\frac{5}{18}\) is wrong because it incorrectly doubles the denominator instead of keeping it constant during subtraction. When subtracting like fractions, only the numerators change; the denominator stays the same.

Multiply straight across: \(\frac{4 \times 5}{5 \times 8} = \frac{20}{40}\), which simplifies to \(\frac{1}{2}\). The choice \(\frac{9}{13}\) is wrong because it results from adding the numerators and denominators instead of multiplying them. When multiplying fractions, multiply numerators together and denominators together, then simplify.

Dividing by a fraction means multiplying by its reciprocal: \(\frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4}\). The choice \(\frac{10}{18}\) is wrong because it multiplies straight across without flipping the second fraction, which is the required step for division. Always flip the divisor and multiply when dividing fractions.

Line up decimal points and subtract: \(2.40 - 0.75 = 1.65\). The choice \(1.75\) is wrong because it results from an arithmetic slip when borrowing across the decimal places. When subtracting decimals, align the decimal points carefully and borrow as needed just like with whole numbers.

\(0.6\) means six tenths, or \(\frac{6}{10}\), which simplifies to \(\frac{3}{5}\) by dividing both terms by 2. The choice \(\frac{6}{10}\) is not in simplest form since both numbers share a common factor. Always reduce fractions from decimal conversions to their lowest terms.

Dividing both numerator and denominator of \(\frac{9}{12}\) by their greatest common factor, 3, gives \(\frac{3}{4}\). The choice \(\frac{6}{9}\) is wrong because although it also simplifies, it is not equal in value to \(\frac{9}{12}\) since \(\frac{6}{9} = \frac{2}{3}\), a different fraction. Always divide by the greatest common factor to find true equivalent fractions in simplest form.

Convert to improper fractions with a common denominator: \(\frac{7}{2} = \frac{21}{6}\) and \(\frac{5}{3} = \frac{10}{6}\), and \(\frac{21}{6} + \frac{10}{6} = \frac{31}{6} = 5\frac{1}{6}\). The choice \(4\frac{3}{5}\) is wrong because it comes from simply adding whole numbers and fraction parts separately without a common denominator. When adding mixed numbers, convert to a common denominator before combining fraction parts.

\(0.375 = \frac{375}{1000}\), and dividing both terms by their greatest common factor, 125, gives \(\frac{3}{8}\). The choice \(\frac{5}{8}\) is wrong because that fraction equals \(0.625\), not \(0.375\). Always simplify decimal-to-fraction conversions fully using the greatest common factor.

When two fractions share the same denominator, the one with the smaller numerator represents a smaller quantity, so \(\frac{2}{7} < \frac{3}{7}\). The choice stating they are equal is wrong because the numerators, 2 and 3, are different, meaning the fractions represent different amounts of the same-sized parts. When denominators match, simply compare the numerators directly.

Multiply as if there were no decimal points, \(12 \times 5 = 60\), then place the decimal based on the total of two decimal places in the factors, giving \(0.60\) or \(0.6\). The choice \(1.7\) is wrong because it results from adding the two numbers instead of multiplying them. When multiplying decimals, count the total decimal places in both factors to correctly place the decimal in the product.

Converting all values to decimals gives \(\frac{2}{5} = 0.4\), \(0.45\), and \(\frac{1}{2} = 0.5\), so the correct ascending order is \(\frac{2}{5}, 0.45, \frac{1}{2}\). The choice ordering \(0.45, \frac{2}{5}, \frac{1}{2}\) is wrong because \(0.45\) is actually greater than \(\frac{2}{5} = 0.4\), not less than it. Converting all values to a common form, like decimals, makes comparing and ordering much easier.

Convert \(\frac{1}{3}\) to twelfths: \(\frac{1}{3} = \frac{4}{12}\), so \(\frac{5}{12} + \frac{4}{12} = \frac{9}{12} = \frac{3}{4}\). The choice \(\frac{6}{15}\) is wrong because it adds the numerators and denominators directly instead of finding a common denominator first. Always identify a common denominator before adding fractions with unlike denominators.

The decimal part \(0.25\) equals \(\frac{25}{100}\), which simplifies to \(\frac{1}{4}\), giving the mixed number \(6\frac{1}{4}\). The choice \(6\frac{25}{100}\) is wrong because although numerically correct, it is not in simplest form since 25 and 100 share common factors. Always simplify the fractional part of a mixed number after converting from a decimal.

Dividing by 2 is the same as multiplying by \(\frac{1}{2}\): \(\frac{5}{6} \times \frac{1}{2} = \frac{5}{12}\). The choice \(\frac{10}{6}\) is wrong because it results from multiplying by 2 instead of dividing, doubling the value rather than halving it. When dividing a fraction by a whole number, multiply by the reciprocal of that whole number.

Convert \(\frac{3}{4}\) to eighths: \(\frac{3}{4} = \frac{6}{8}\), so \(\frac{7}{8} - \frac{6}{8} = \frac{1}{8}\). The choice \(\frac{1}{4}\) is wrong because it results from subtracting numerators and denominators without first converting to a common denominator. Always convert unlike fractions to a shared denominator before subtracting.

Since \(20 \times 5 = 100\), multiply both numerator and denominator by 5 to get \(\frac{45}{100} = 0.45\). The choice \(0.9\) is wrong because it comes from mistakenly treating the denominator as if it were 10 instead of 20. When the denominator is a factor of 100, scale both numerator and denominator to create an equivalent fraction over 100.

Making half the recipe means multiplying the original amount by \(\frac{1}{2}\): \(\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\) cup. The choice \(\frac{1}{2}\) cup is wrong because it ignores the original fraction amount and just uses the scaling factor as the answer. When scaling a recipe, multiply each ingredient amount by the scaling fraction to get the new quantity.

Convert \(2\frac{1}{4}\) to an improper fraction, \(\frac{9}{4}\), then multiply: \(\frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2}\). The choice \(\frac{9}{12}\) is wrong because it stops at multiplying only part of the fraction and does not correctly multiply straight across both numerators and denominators before simplifying. Always convert mixed numbers to improper fractions before multiplying.

You ate \(\frac{3}{8}\) of the pizza, leaving \(\frac{5}{8}\), which as a decimal is \(5 \div 8 = 0.625\). The choice \(0.375\) is wrong because that represents the fraction eaten, \(\frac{3}{8}\), rather than the fraction remaining. Always identify what quantity the question asks for, whether it's the part used or the part remaining, before converting to a decimal.

Convert to improper fractions with a common denominator: \(\frac{14}{3} = \frac{28}{6}\) and \(\frac{11}{6}\), so \(\frac{28}{6} - \frac{11}{6} = \frac{17}{6} = 2\frac{5}{6}\). The choice \(3\frac{1}{6}\) is wrong because it results from subtracting the fraction parts without properly borrowing when the second fraction part is larger, or from a common denominator error. When subtracting mixed numbers, convert fully to improper fractions to avoid borrowing mistakes.

Dividing 7 by 16 gives exactly \(0.4375\), and rounding to the nearest thousandth means looking at the ten-thousandths digit, 5, which rounds the thousandths digit up from 7 to 8, giving \(0.438\). The choice claiming \(0.4375\) rounds to \(0.437\) is wrong because a digit of 5 or higher in the rounding position always rounds up, not down. Always check the digit immediately to the right of the desired rounding place to decide whether to round up or keep the digit the same.

Converting all to decimals gives \(\frac{5}{6} \approx 0.833\), \(0.8\), and \(\frac{7}{9} \approx 0.778\), so from greatest to least the order is \(\frac{5}{6}, 0.8, \frac{7}{9}\). The choice \(0.8, \frac{5}{6}, \frac{7}{9}\) is wrong because \(\frac{5}{6} \approx 0.833\) is actually larger than \(0.8\), not smaller. When comparing multiple values in different forms, convert everything to decimals with enough precision to distinguish close values.

Convert to improper fractions with a common denominator of 12: \(2\frac{1}{3} = \frac{28}{12}\) and \(1\frac{3}{4} = \frac{21}{12}\), so the difference is \(\frac{28}{12} - \frac{21}{12} = \frac{7}{12}\) cup. The choice \(\frac{2}{3}\) cup is wrong because it results from an incorrect subtraction that does not use a proper common denominator of 12 for both mixed numbers. When solving real-world subtraction problems with mixed numbers, always convert to a common denominator before subtracting.

First square the fraction, \(\left(\frac{3}{4}\right)^2 = \frac{9}{16}\), then add \(\frac{1}{2} = \frac{8}{16}\) to get \(\frac{9}{16} + \frac{8}{16} = \frac{17}{16}\). The choice \(\frac{5}{4}\) is wrong because it comes from squaring only the numerator or mishandling the order of operations, missing the correct exponentiation step first. Following order of operations, always evaluate exponents on fractions before performing addition or subtraction.

Convert \(0.6\) to a fraction, \(\frac{3}{5} = \frac{9}{15}\), and \(\frac{1}{3} = \frac{5}{15}\), so their sum is \(\frac{9}{15} + \frac{5}{15} = \frac{14}{15}\). The choice \(1\) is wrong because it incorrectly assumes the two values round or combine to a whole, but \(\frac{14}{15}\) is close to but not equal to 1. When adding a decimal and a fraction, convert both to the same form, either fractions or decimals, before combining.

Convert both mixed numbers to improper fractions, \(\frac{16}{5}\) and \(\frac{8}{5}\), then multiply by the reciprocal: \(\frac{16}{5} \times \frac{5}{8} = \frac{80}{40} = 2\). The choice \(\frac{1}{2}\) is wrong because it results from flipping the wrong fraction, dividing the second by the first instead of the first by the second. When dividing mixed numbers, always convert to improper fractions first, then multiply by the reciprocal of the divisor.

\(0.45\) converts to \(\frac{45}{100} = \frac{9}{20}\), which is not equal to \(\frac{2}{5} = 0.4\), making it the value that does not match. The choice \(0.4\) is wrong to select because it is exactly equal to \(\frac{2}{5}\), both representing four-tenths of a whole. When checking equivalence between decimals and fractions, always convert both to a common form, like decimals, and compare their exact values.

Find a common denominator of 12: \(\frac{5}{6} = \frac{10}{12}\) and \(\frac{3}{4} = \frac{9}{12}\), so their sum is \(\frac{19}{12} = 1\frac{7}{12}\) meters. The choice \(1\frac{1}{2}\) meters is wrong because it likely results from rounding or averaging the two fractions instead of correctly adding them with a common denominator. When solving word problems involving combined lengths, convert to a common denominator and add exactly rather than estimating.

Dividing 2 by 9 produces a repeating pattern of the digit 2 forever, written as \(0.\overline{2}\), since ninths always create single-digit repeating decimals. The choice \(0.2\) is wrong because it terminates the decimal instead of showing that the 2 repeats infinitely, giving a slightly inaccurate value. Fractions with denominators like 9, 99, or 999 often produce repeating decimal patterns that should be marked with a bar over the repeating digits.

Convert \(\frac{1}{4}\) to eighths, \(\frac{2}{8}\), then add to the original amount: \(\frac{3}{8} + \frac{2}{8} = \frac{5}{8}\). The choice \(\frac{1}{2}\) is wrong because it approximates the sum instead of using the exact common denominator calculation, which yields \(\frac{5}{8}\), not \(\frac{4}{8}\). In real-world fraction addition problems, always find the exact common denominator rather than estimating the result.

Dividing by a fraction means multiplying by its reciprocal: \(5 \times \frac{3}{2} = \frac{15}{2}\). The choice \(\frac{10}{3}\) is wrong because it results from multiplying 5 by \(\frac{2}{3}\) directly instead of by its reciprocal \(\frac{3}{2}\). When dividing a whole number by a fraction, rewrite the whole number as a fraction over 1 and multiply by the reciprocal of the divisor.

A fraction produces a terminating decimal only when its denominator in simplest form has prime factors of just 2 and/or 5, and since 8 equals \(2^3\), \(\frac{3}{8} = 0.375\) terminates. The choice \(\frac{1}{6}\) is wrong because 6 has a prime factor of 3, which causes the decimal \(0.1\overline{6}\) to repeat forever. To predict whether a fraction terminates, check whether its denominator's prime factorization contains only 2s and 5s.

Convert all fractions to tenths: \(\frac{9}{10} - \frac{6}{10} + \frac{5}{10} = \frac{8}{10} = \frac{4}{5}\). The choice \(\frac{7}{10}\) is wrong because it likely comes from a sign or arithmetic error when combining the three terms in sequence. When solving multi-step fraction expressions, convert every term to a common denominator first and then perform operations strictly in left-to-right order.

The empty amount is \(12\frac{1}{2} - 3\frac{3}{4} = 8\frac{3}{4}\) gallons, and dividing by the total capacity, \(8.75 \div 12.5 = 0.70\), gives the fraction of the tank that is empty. The choice \(0.30\) is wrong because it represents the fraction of the tank that is filled rather than empty, mixing up which quantity the question asked for. In multi-step word problems, always identify the specific quantity requested before finalizing calculations.