ASVAB Fractions and Decimals: A Worked Review

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Use the size of the number as your first check

ASVAB fractions and decimals practice is easier when you understand what each number represents. A fraction names parts of a whole; a decimal uses place value to express those parts. Before applying a rule, estimate whether the quantity is smaller than one, near one, or several wholes. That quick judgment helps catch misplaced decimals and inverted fractions.

Three quarters is 0.75, which is less than one but more than one half. Seven fourths is 1.75, so it must exceed one. A calculation that turns either into 7.5 needs checking. Keep common equivalents such as 1/2 = 0.5, 1/4 = 0.25, and 1/5 = 0.2 available in memory through use, not only through reciting a chart.

These foundations support both direct mathematics questions and Arithmetic Reasoning word problems. Practice the operation alone, then put it back into a short story with units.

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Adding and subtracting require equal-sized parts

To add 1/3 and 1/4, use a common denominator of 12. One third becomes 4/12 and one fourth becomes 3/12. Their sum is 7/12. Adding the original numerators and denominators would give 2/7, which is smaller than either original fraction and cannot be their positive sum.

For 5/6 − 1/4, use twelfths: 10/12 − 3/12 = 7/12. The denominator stays 12 because you are still counting twelfths. Reduce the final fraction if a common factor remains. Six twelfths equals one half because both numerator and denominator divide by six.

Use the least common denominator when convenient, but any common denominator works. A larger one may create extra arithmetic; it does not make the method wrong. Focus first on preserving the value of each fraction while changing its form.

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Multiplication, division, and mixed numbers

For multiplication, multiply numerators together and denominators together: 2/3 × 3/5 = 6/15 = 2/5. You can cancel common factors across the product first to reduce arithmetic. Cancellation means dividing a numerator and a denominator by the same nonzero factor; it does not mean deleting matching digits.

For division, multiply by the reciprocal of the divisor: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2. The result answers how many halves fit into three quarters: one and a half. Dividing by a positive number smaller than one can increase the numerical value, so do not assume every division makes a number smaller.

Convert mixed numbers to improper fractions before multiplying. Two and one third becomes 7/3 because two wholes contain six thirds plus one more third. Then 2 1/3 × 3/7 = 7/3 × 3/7 = 1. Reversing the conversion gives a final mixed number when the question asks for that form.

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Decimal place value and conversion

When adding decimals, align decimal points: 2.4 + 0.37 becomes 2.40 + 0.37 = 2.77. Aligning the final digits instead of place values would mix tenths and hundredths. Zeros can clarify the alignment without changing the number.

For 0.6 × 0.08, first calculate 6 × 8 = 48. The original factors have three total decimal places, giving 0.048. The estimate confirms it: multiplying 0.6 by a small fraction of one should produce a much smaller number than 0.6.

To convert 0.375 to a fraction, write 375/1000 and reduce to 3/8. To convert 3/8 to a decimal, divide three by eight. For 4.8 ÷ 0.12, multiply both quantities by 100, producing 480 ÷ 12 = 40. Scaling both quantities equally preserves the quotient.

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A short sequence for rebuilding fluency

Start with equivalent fractions and simplification, then addition and subtraction, then multiplication and division. Add mixed numbers after the basic operations are comfortable. Finish with a mixed set so the symbol, rather than the section heading, determines the method.

Explain the reason for the rule aloud. For addition, you need equal-sized parts. For division, you are measuring how many groups of the divisor fit into the dividend. If you can describe the meaning, you are less likely to apply a remembered rule to the wrong operation.