Worksheet · Fraction Multiplication · 1 of 6
Roots of Reason
Name
Date
Fraction of a Whole Number
1/2 × 6 asks for half of 6. The word of does the work.
1.1/2 × 6. Six counters. Click to shade half of them, then count the shaded ones.
12 × 6 =
2.1/3 × 12, then use that answer for 2/3 × 12. Two thirds is just two of the one-third answer.
13 × 12 =
23 × 12 =
3.3/4 × 8. Find one fourth first, then take three of them.
14 × 8 =
three of them:
34 × 8 =
Multiplying by a fraction less than 1 takes a part, so the answer shrinks.
Worksheet · Fraction Multiplication · 2 of 6
Roots of Reason
Name
Date
Fraction of a Fraction
Shade one fraction, then shade the other on top. The overlap is the answer.
1.1/2 × 1/3. The grid shows thirds across and halves down. One third is shaded light. Half of it is shaded deep. Count: the deep piece is 1 of how many equal pieces?
12 × 13 =
2.1/2 × 3/4. Fourths across, halves down. Click to shade 3/4 of the top row only. That is half of three fourths. Count your shaded pieces out of the whole grid.
12 × 34 =
3.Look at both grids. Where do the denominators of the answers (6 and 8) come from?
The grid multiplies the denominators for you: rows × columns.
Worksheet · Fraction Multiplication · 3 of 6
Roots of Reason
Name
Date
Multiply Across
Tops together, bottoms together. Simplify if you can.
1.Multiply across. Type fraction answers like 3/8, and simplify where you can.
12 × 13 =
23 × 34 =
4 × 25 =
56 × 1 =
2.3/4 × 8/9. Multiply across, then simplify the result.
tops: 3 × 8 =
bottoms: 4 × 9 =
simplified:
3.Find the flaw. A student computes 1/2 × 1/3 by multiplying the tops and adding the bottoms, and gets 1/5. Use the grid from page 2 to explain what the bottoms really do.
The bottoms multiply because cutting cuts every piece again.
Worksheet · Fraction Multiplication · 4 of 6
Roots of Reason
Name
Date
Break Apart Mixed Numbers
Same move as 83 × 2: split, multiply the pieces, add.
1.2 1/2 × 3. The split is written for you. Type mixed numbers like 7 1/2.
2 12 × 3 = (2 × 3) + (12 × 3) = + =
2.3 1/4 × 2. Write the split yourself this time.
3 14 × 2 = ( × 2) + ( × 2) = + =
3.1 2/3 × 6. Split it, show both pieces in the work space, add.
1 23 × 6 =
A mixed number is already split: a whole part and a fraction part. Use it.
Worksheet · Fraction Multiplication · 5 of 6
Roots of Reason
Name
Date
Improper Fractions First
When both numbers are mixed, rename them as fractions, then multiply across.
1.Rename each mixed number as an improper fraction.
1 12 =
2 23 =
3 14 =
2.1 1/2 × 2 2/3. You just renamed both. Multiply across, then simplify.
32 × 83 = =
3.2 1/2 × 1 1/5. Rename both, multiply across, simplify. Show every step in the work space.
renamed: ×
answer:
2 2/3 and 8/3 are two names for the same number. Pick the name that multiplies cleanly.
Worksheet · Fraction Multiplication · 6 of 6
Roots of Reason
Name
Date
Fraction Multiplication Stories
For each story: write the equation, show your work, answer with a unit.
1.A recipe needs 3/4 cup of flour. You make half the recipe. How much flour?
equation: answer:
2.A garden bed is 2 1/2 meters long and 3 meters wide. What is its area?
equation: answer:
3.A hiker walks 2/3 mile every day for 6 days. How far in all?
equation: answer:
Story 1 shrinks, stories 2 and 3 grow. The fraction tells you which way before you compute.