GED Mathematical Reasoning
Fractions & Decimals
A fraction is a division waiting to happen: 3/4 means 3 divided by 4. The bottom number says how many equal pieces one whole was cut into; the top says how many of those pieces you have. A decimal is the same idea written differently — 0.75 is 75 hundredths, which is the same amount as 3/4.
The words first
- numerator
- the top number — how many pieces you have
- denominator
- the bottom number — how many pieces make one whole
- common denominator
- the same bottom number on both fractions, so the pieces are the same size
- simplify / reduce
- divide top and bottom by the same number to write it smaller
The method
ADDING OR SUBTRACTING FRACTIONS
You cannot add pieces of different sizes.
1. Make the bottoms match.
2. Add or subtract the tops only.
3. Leave the bottom alone.
1/4 + 1/6
bottoms 4 and 6 both divide into 12
1/4 = 3/12 1/6 = 2/12
3/12 + 2/12 = 5/12
MULTIPLYING FRACTIONS (easier — no common denominator needed)
2/3 × 4/5 = (2×4)/(3×5) = 8/15
DIVIDING FRACTIONS — flip the second one and multiply
2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
FRACTION TO DECIMAL — just divide
3/4 = 3 ÷ 4 = 0.75
Worked all the way through
The problem
A recipe calls for 2/3 cup of flour. You are making one and a half times the recipe. How much flour?
- Step 1 — Write the words as math.One and a half times 2/3 means 1½ × 2/3.
- Step 2 — Turn the mixed number into a fraction.1½ = 3/2, because two halves make one whole plus one more half is three halves.
- Step 3 — Multiply straight across.3/2 × 2/3 = (3×2)/(2×3) = 6/6
- Step 4 — Simplify.6/6 = 1
On the board
1½ × 2/3
the problem
3/2 × 2/3
1½ rewritten as a fraction
(3 × 2) / (2 × 3)
multiply straight across
6/6
1
6 divided by 6
Answer
1 cup
A second one, in a different form
What is 3/4 − 1/6?
3/4 − 1/6
the problem
9/12 − 2/12
both bottoms become 12
7/12
subtract the tops only
Answer
7/12
The usual mistake
Adding the denominators. 2/3 + 1/4 is never 3/7.
Check yourself
Check it against common sense: one and a half times two-thirds should be more than two-thirds but not much more. 1 cup fits.
Practice it
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