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Inch Fraction worksheet

Grades 5–6 · CCSS 5.NF.B.3, 6.RP.A.3.d

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Convert: Fraction of an inch → decimal and mm
- Inches as a fraction: 1 4/16
Find: Decimal inches
Answer
2.
Problem 2.
- Convert: Fraction of an inch → decimal and mm
- Inches as a fraction: 1 4/12
Find: Decimal inches
Answer
3.
Problem 3.
- Convert: Decimal or metric → fraction of an inch
- Measurement: 30 mm
- Round to the nearest: 1/64 inch
Find: Nearest 1/64 inch
Answer
4.
Problem 4.
- Convert: Decimal or metric → fraction of an inch
- Measurement: 28 mm
- Round to the nearest: 1/2 inch
Find: Nearest 1/2 inch
Answer
5.
Problem 5.
- Convert: Decimal or metric → fraction of an inch
- Measurement: 30 mm
- Round to the nearest: 1/4 inch
Find: Nearest 1/4 inch
Answer
6.
Problem 6.
- Convert: Decimal or metric → fraction of an inch
- Measurement: 42 mm
- Round to the nearest: 1/4 inch
Find: Nearest 1/4 inch
Answer
7.
Problem 7.
- Convert: Fraction of an inch → decimal and mm
- Inches as a fraction: 1 5/16
Find: Decimal inches
Answer
8.
Problem 8.
- Convert: Decimal or metric → fraction of an inch
- Measurement: 28 mm
- Round to the nearest: 1/32 inch
Find: Nearest 1/32 inch
Answer
9.
Problem 9.
- Convert: Decimal or metric → fraction of an inch
- Measurement: 29 mm
- Round to the nearest: 1/32 inch
Find: Nearest 1/32 inch
Answer
10.
Problem 10.
- Convert: Fraction of an inch → decimal and mm
- Inches as a fraction: 2 2/16
Find: Decimal inches
Answer

Answer key: Inch Fraction worksheet

1. Decimal inches: 1.25
1. Divide the top number of the fraction by the bottom number to get a decimal, then add the whole inches
  $1 +$ $= \frac{4}{16}$ $= 1.25 in$
2. Multiply by 25.4 to get millimeters, because an inch is exactly 25.4 mm
  $1.25 \times 25.4$ $= 31.75 mm$
3. Simplify the fraction (lowest terms)
  $1 1/4 in$
2. Decimal inches: 1.333333
1. Divide the top number of the fraction by the bottom number to get a decimal, then add the whole inches
  $1 +$ $= \frac{4}{12}$ $= 1.333333 in$
2. Multiply by 25.4 to get millimeters, because an inch is exactly 25.4 mm
  $1.333333 \times 25.4$ $= 33.8667 mm$
3. Simplify the fraction (lowest terms)
  $1 1/3 in$
3. Nearest 1/64 inch: 1 3/16 in
1. Convert to inches: 1 in = 25.4 mm exactly
  $\frac{30}{25.4}$ $= 1.181102 in$
2. Count how many 1/64ths of an inch fit: multiply the inches by 64 and round to the nearest whole number, which picks the nearest mark
  $1.181102 \times 64$ $= 75.5906$ $= rounded: 76$
3. Split off the whole inches and reduce the fraction to lowest terms
  $\frac{76}{64}$ $= 1 3/16 in$
4. Find the rounding error: the rounded mark minus the exact length, so you know how close the mark is
  $1.1875 - 1.181102$ $= 0.006398 in$ $= = 0.1625 mm$
4. Nearest 1/2 inch: 1 in
1. Convert to inches: 1 in = 25.4 mm exactly
  $\frac{28}{25.4}$ $= 1.102362 in$
2. Count how many 1/2ths of an inch fit: multiply the inches by 2 and round to the nearest whole number, which picks the nearest mark
  $1.102362 \times 2$ $= 2.2047$ $= rounded: 2$
3. Split off the whole inches and reduce the fraction to lowest terms
  $\frac{2}{2}$ $= 1 in$
4. Find the rounding error: the rounded mark minus the exact length, so you know how close the mark is
  $1 - 1.102362$ $= −0.102362 in$ $= = −2.6 mm$
5. Nearest 1/4 inch: 1 1/4 in
1. Convert to inches: 1 in = 25.4 mm exactly
  $\frac{30}{25.4}$ $= 1.181102 in$
2. Count how many 1/4ths of an inch fit: multiply the inches by 4 and round to the nearest whole number, which picks the nearest mark
  $1.181102 \times 4$ $= 4.7244$ $= rounded: 5$
3. Split off the whole inches and reduce the fraction to lowest terms
  $\frac{5}{4}$ $= 1 1/4 in$
4. Find the rounding error: the rounded mark minus the exact length, so you know how close the mark is
  $1.25 - 1.181102$ $= 0.068898 in$ $= = 1.75 mm$
6. Nearest 1/4 inch: 1 3/4 in
1. Convert to inches: 1 in = 25.4 mm exactly
  $\frac{42}{25.4}$ $= 1.653543 in$
2. Count how many 1/4ths of an inch fit: multiply the inches by 4 and round to the nearest whole number, which picks the nearest mark
  $1.653543 \times 4$ $= 6.6142$ $= rounded: 7$
3. Split off the whole inches and reduce the fraction to lowest terms
  $\frac{7}{4}$ $= 1 3/4 in$
4. Find the rounding error: the rounded mark minus the exact length, so you know how close the mark is
  $1.75 - 1.653543$ $= 0.096457 in$ $= = 2.45 mm$
7. Decimal inches: 1.3125
1. Divide the top number of the fraction by the bottom number to get a decimal, then add the whole inches
  $1 +$ $= \frac{5}{16}$ $= 1.3125 in$
2. Multiply by 25.4 to get millimeters, because an inch is exactly 25.4 mm
  $1.3125 \times 25.4$ $= 33.3375 mm$
8. Nearest 1/32 inch: 1 3/32 in
1. Convert to inches: 1 in = 25.4 mm exactly
  $\frac{28}{25.4}$ $= 1.102362 in$
2. Count how many 1/32ths of an inch fit: multiply the inches by 32 and round to the nearest whole number, which picks the nearest mark
  $1.102362 \times 32$ $= 35.2756$ $= rounded: 35$
3. Split off the whole inches and reduce the fraction to lowest terms
  $\frac{35}{32}$ $= 1 3/32 in$
4. Find the rounding error: the rounded mark minus the exact length, so you know how close the mark is
  $1.09375 - 1.102362$ $= −0.008612 in$ $= = −0.2188 mm$
9. Nearest 1/32 inch: 1 5/32 in
1. Convert to inches: 1 in = 25.4 mm exactly
  $\frac{29}{25.4}$ $= 1.141732 in$
2. Count how many 1/32ths of an inch fit: multiply the inches by 32 and round to the nearest whole number, which picks the nearest mark
  $1.141732 \times 32$ $= 36.5354$ $= rounded: 37$
3. Split off the whole inches and reduce the fraction to lowest terms
  $\frac{37}{32}$ $= 1 5/32 in$
4. Find the rounding error: the rounded mark minus the exact length, so you know how close the mark is
  $1.15625 - 1.141732$ $= 0.014518 in$ $= = 0.3688 mm$
10. Decimal inches: 2.125
1. Divide the top number of the fraction by the bottom number to get a decimal, then add the whole inches
  $2 +$ $= \frac{2}{16}$ $= 2.125 in$
2. Multiply by 25.4 to get millimeters, because an inch is exactly 25.4 mm
  $2.125 \times 25.4$ $= 53.975 mm$
3. Simplify the fraction (lowest terms)
  $2 1/8 in$