Fractions: make the pieces the same size.
A fraction names a number of equal-sized parts. Before adding or subtracting fractions, make sure the parts are the same size.
Reviewed · Official ASVAB scope and calculator guidance. Examples are original AptiStep material.
Start with what the denominator means
In 3/4, the denominator 4 says that one whole has been divided into four equal pieces. The numerator 3 says how many pieces you have. In 1/8, the pieces are smaller. Adding three quarter-sized pieces and one eighth-sized piece does not give four twelfth-sized pieces.
An equivalent fraction changes the way a value is written without changing the value. Multiplying both the numerator and denominator by the same nonzero number preserves the fraction: 3/4 = 6/8.
Multiplication answers a different question
To find 2/3 of 18, divide 18 into three equal parts and take two of them: 18 ÷ 3 × 2 = 12. You can also write (2 × 18)/3. “Of” often signals multiplication in a fraction question, but read the whole sentence to check what quantity is requested.
Try a fresh example
Find 1/2 + 1/6 before opening the explanation.
Show the solution
Use sixths: 1/2 = 3/6. Then 3/6 + 1/6 = 4/6. Divide the numerator and denominator by 2 to simplify: 2/3.
What to write in your review note
If you added the denominators, write “Match the piece size before adding.” If you found 4/6 but did not simplify, the value is still correct; practice recognizing an equivalent simplest form. Explain the operation in words, then solve another example without looking back.
Four fresh questions
Try each example before opening its answer. Then explain the step you used in your own words.
What is 5/6 − 1/4?
Show answer and reasoning
7/12
Use twelfths: 5/6 = 10/12 and 1/4 = 3/12. Subtract 10 − 3 while keeping the denominator 12. The answer is smaller than 5/6, as subtraction requires.
Find 3/5 of 25.
Show answer and reasoning
15
One fifth of 25 is 5. Take three of those groups: 3 × 5 = 15. “Of” describes a part of the original quantity here.
A recipe needs 3/4 cup of milk. You make half the recipe. How much milk is needed?
Show answer and reasoning
3/8 cup
Halve each of the three quarter-cup portions: (3/4) × (1/2) = 3/8. Half a quantity must be smaller than the original quantity.
Which is larger: 7/10 or 2/3?
Show answer and reasoning
7/10
Compare equal-sized thirtieths: 7/10 = 21/30 and 2/3 = 20/30. The first fraction has one more thirtieth. Comparing numerators alone would not work with the original denominators.
Can you explain the method without looking?
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