Fractions, Decimals and Ratios: A Trade Math Worksheet
Practise fractions, decimals, ratios and percentage allowances with original trade math problems, clear worked answers and simple checks for common mistakes.
Fractions, decimals and ratios become easier when you decide what the numbers describe before calculating. A length, a share of a total and a percentage allowance need different setups, even when a calculator accepts the same digits.
This trade math worksheet uses invented dimensions and quantities. Every length is an actual stated measurement; none is a nominal pipe size. The examples are arithmetic exercises, with any allowance stated in the question.
If changing units is the difficult part, start with the unit conversions lesson. Here, the focus is choosing operations and checking whether an answer makes sense.
One measurement, two useful forms
A drawing exercise gives a strip length of 2 3/8 in. A worksheet asks for decimal inches.
Keep the whole number and convert the fraction:
3 ÷ 8 = 0.375
2 + 0.375 = 2.375 in
The reverse direction is just as useful. Suppose a dimension is 0.6875 in. Multiplying its fractional part by 16 gives 11, so the dimension is 11/16 in.
Check the result by dividing 11 by 16. You should return to 0.6875. This reverse check catches a misplaced digit without needing a memorized conversion table.
A decimal with many digits is not automatically a more accurate measurement. In these exercises the values are given exactly for arithmetic practice; a real measurement also depends on the measuring process.
Add the lengths before rounding
A paper layout combines a 1 5/8 in segment with a 2 3/4 in segment. What is the total?
Change only the fractional parts to a shared denominator:
1 5/8 + 2 6/8 = 3 + 11/8 = 4 3/8 in
Alternatively:
1.625 + 2.75 = 4.375 in
Both routes give the same length. An estimate provides another check: the first segment exceeds 1.5 inches and the second exceeds 2.5 inches, so the answer must exceed 4 inches.
Now consider a repeated decimal. One third of 9 inches is exactly 3 inches. Entering 0.33 × 9 gives 2.97 instead. Keeping the fraction until the final calculation avoids introducing that rounding error.
Write a line explaining your choice: “I kept one third as a fraction because its decimal repeats.” That explanation is more useful than simply circling a calculator answer.
A ratio describes a relationship
An imaginary training board has two coloured regions in a width ratio of 2:3. Their combined width is 35 cm. Find each width.
The ratio contains five equal shares altogether:
One share: 35 ÷ 5 = 7 cm
First region: 2 × 7 = 14 cm
Second region: 3 × 7 = 21 cm
Two checks confirm the result: 14 + 21 = 35, and 14:21 simplifies to 2:3.
The first region is 2/5 of the total, not 2/3. The fraction 2/3 compares the first region with the second region. This distinction matters whenever a question asks for a share of a combined amount.
State the quantities behind a ratio. NIST explains that ratios between quantities of the same kind can retain unit notation, such as m/m, to make their meaning clear. Our width comparison is one length divided by another. NIST SI guidance on quantities and ratios.
Percentage allowance: identify the starting amount
A worksheet calls for 48 m of an imaginary material plus an 8% allowance. The stated allowance applies to the original 48 m.
Allowance = 48 × 0.08 = 3.84 m
Combined amount = 48 + 3.84 = 51.84 m
A quick check is to calculate 10% first: 4.8 m. The 8% allowance must be smaller.
This is a mathematical allowance chosen for the exercise, not a recommended waste factor. If a question supplies a different basis for its percentage, write that basis down before multiplying.
Try four questions without the worked answers
Express 7/16 + 0.375 as a decimal and a fraction.
A paper dimension is 5.25 in. Subtract 5/8 in. What remains?
Two sections have a length ratio of 6:9 and a combined length of 45 cm. Find each length.
Add a stated 12% allowance to a base quantity of 80 units.
Answers
0.4375 + 0.375 = 0.8125 = 13/16.
5.25 − 0.625 = 4.625 in = 4 5/8 in.
There are 15 shares, each 3 cm: 18 cm and 27 cm.
The allowance is 9.6 units, giving 89.6 units.
For each answer, add one estimate or reverse calculation. If you missed a question, record whether the problem was conversion, operation choice or arithmetic. Keep that note alongside your daily study plan, then return to relevant practice through the G3 module overview.