Multiplying Fractions with Whole Numbers Worksheets - 15 ... - Free Printable

Explanation:
We are multiplying a whole number by a fraction. Here’s how to do it step by step:

1. Write the whole number as a fraction (e.g., 3 = 3/1).
2. Multiply the numerators (top numbers) together.
3. Multiply the denominators (bottom numbers) together.
4. Simplify the result to simplest form (reduce if possible, or write as a mixed number if improper — but here all results will be proper fractions or whole numbers, and we’ll check).

Let’s solve each one carefully:

1. $3 \times \frac{7}{8} = \frac{3}{1} \times \frac{7}{8} = \frac{21}{8}$
Wait — 21/8 is an improper fraction. But the problem says “write in simplest form.” Let’s double-check:
Actually, 3 × 7 = 21, denominator stays 8 → $\frac{21}{8}$. That’s already simplified (21 and 8 share no common factors), but is it expected as improper or mixed? The worksheet shows blank lines like “___ = ___”, likely expecting improper fraction simplified (or maybe mixed). However, looking at other problems, many will give whole numbers or proper fractions. Let’s compute all first.

Wait — re-read instruction: “Multiply and write in simplest form.” In elementary math, *simplest form* for a fraction means reduced (lowest terms), but if it's improper, sometimes they accept improper unless told to convert. However, let’s check each product — maybe most are whole numbers or proper fractions.

Let’s compute each:

1. $3 \times \frac{7}{8} = \frac{21}{8}$ → cannot reduce; simplest form is $\frac{21}{8}$ (or $2\frac{5}{8}$). But since the worksheet has only two blanks per line (“= ___ = ___”), maybe first blank is unsimplified intermediate (like 21/8), second is simplified? But instruction says “Multiply and write in simplest form” — probably just final answer in simplest form. However, the format shows two equals signs: e.g., “3 × 7/8 = ____ = ____”. Likely: first blank = multiplication result before simplifying (e.g., 21/8), second = simplified (but 21/8 is already simplified). Hmm.

Wait — look at problem 4: $4 \times \frac{6}{7} = \frac{24}{7}$ — also improper.

But maybe some simplify to whole numbers! Let’s check:

2. $7 \times \frac{5}{9} = \frac{35}{9}$ → no simplification.

3. $5 \times \frac{3}{7} = \frac{15}{7}$

4. $4 \times \frac{6}{7} = \frac{24}{7}$

5. $3 \times \frac{3}{5} = \frac{9}{5}$

6. $8 \times \frac{4}{7} = \frac{32}{7}$

7. $6 \times \frac{3}{7} = \frac{18}{7}$

None simplify to whole numbers. But wait — maybe I made a mistake. Let’s double-check problem 4: 4 × 6/7 = 24/7 — yes.

Hold on — perhaps the worksheet expects the answer as a mixed number for improper fractions? That’s common in grade 5–6.

Let’s convert each improper fraction to mixed number (if numerator > denominator), and ensure it's in simplest form (fraction part reduced):

1. $21/8 = 2 \frac{5}{8}$
2. $35/9 = 3 \frac{8}{9}$
3. $15/7 = 2 \frac{1}{7}$
4. $24/7 = 3 \frac{3}{7}$
5. $9/5 = 1 \frac{4}{5}$
6. $32/7 = 4 \frac{4}{7}$
7. $18/7 = 2 \frac{4}{7}$

All fractional parts are already in lowest terms (5 & 8 coprime, 8 & 9 coprime, etc.).

But the worksheet has two blanks per line: “= ____ = ____”. Possibly:
- First blank: the product as improper fraction
- Second blank: simplified form (mixed number)

That matches common worksheet design.

So for each, we’ll fill:
1. $3 \times \frac{7}{8} = \frac{21}{8} = 2\frac{5}{8}$
2. $7 \times \frac{5}{9} = \frac{35}{9} = 3\frac{8}{9}$
3. $5 \times \frac{3}{7} = \frac{15}{7} = 2\frac{1}{7}$
4. $4 \times \frac{6}{7} = \frac{24}{7} = 3\frac{3}{7}$
5. $3 \times \frac{3}{5} = \frac{9}{5} = 1\frac{4}{5}$
6. $8 \times \frac{4}{7} = \frac{32}{7} = 4\frac{4}{7}$
7. $6 \times \frac{3}{7} = \frac{18}{7} = 2\frac{4}{7}$

Let me verify each multiplication again:

1. 3×7=21, /8 → 21/8 ✔
2. 7×5=35, /9 → 35/9 ✔
3. 5×3=15, /7 → 15/7 ✔
4. 4×6=24, /7 → 24/7 ✔
5. 3×3=9, /5 → 9/5 ✔
6. 8×4=32, /7 → 32/7 ✔
7. 6×3=18, /7 → 18/7 ✔

Mixed numbers:
1. 21 ÷ 8 = 2 remainder 5 → 2 5/8 ✔
2. 35 ÷ 9 = 3 r8 → 3 8/9 ✔
3. 15 ÷ 7 = 2 r1 → 2 1/7 ✔
4. 24 ÷ 7 = 3 r3 → 3 3/7 ✔
5. 9 ÷ 5 = 1 r4 → 1 4/5 ✔
6. 32 ÷ 7 = 4 r4 → 4 4/7 ✔
7. 18 ÷ 7 = 2 r4 → 2 4/7 ✔

All correct.

Final Answer:
1. $\frac{21}{8} = 2\frac{5}{8}$
2. $\frac{35}{9} = 3\frac{8}{9}$
3. $\frac{15}{7} = 2\frac{1}{7}$
4. $\frac{24}{7} = 3\frac{3}{7}$
5. $\frac{9}{5} = 1\frac{4}{5}$
6. $\frac{32}{7} = 4\frac{4}{7}$
7. $\frac{18}{7} = 2\frac{4}{7}$