ASVAB Study Guide4. Dividing Decimals
Adding numbers with decimal points
$$a.b + c.d$$
Align the decimal points. Add as with whole numbers, keeping the decimal point aligned in the sum.
Example
Calculate: $$12.45 + 3.8$$
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Line up decimal points: $$12.45 + 3.80 = 16.25$$
Practice problems
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Problem 1
Calculate: $$4.2 + 3.5$$
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Answer: 7.7
Align decimal points: $$4.2 + 3.5 = 7.7$$
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Problem 2
Calculate: $$15.68 + 7.4$$
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Answer: 23.08
Pad zero: $$15.68 + 7.40 = 23.08$$
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Problem 3
Calculate: $$104.5 + 28.75 + 3.02$$
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Answer: 136.27
Align all decimal points: $$104.50 + 28.75 + 3.02 = 136.27$$
Subtracting numbers with decimal points
$$a.b - c.d$$
Align the decimal points. Add zeros to the right if necessary. Subtract as with whole numbers.
Example
Calculate: $$15.4 - 6.25$$
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Pad zero: $$15.40 - 6.25 = 9.15$$
Practice problems
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Problem 4
Calculate: $$8.9 - 3.4$$
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Answer: 5.5
Subtract directly: $$8.9 - 3.4 = 5.5$$
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Problem 5
Calculate: $$20.5 - 8.35$$
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Answer: 12.15
Pad zero: $$20.50 - 8.35 = 12.15$$
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Problem 6
Calculate: $$50 - 18.64$$
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Answer: 31.36
Rewrite as 50.00: $$50.00 - 18.64 = 31.36$$
Multiplying two decimal numbers
$$a.b \times c.d$$
Multiply as with whole numbers. Count the sum of the decimal places of both numbers and place the decimal point in the product.
Example
Calculate: $$2.3 \times 1.4$$
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1) $$23 \times 14 = 322$$.
2) $$1 + 1 = 2$$ decimal places.
3) Result = 3.22.
Practice problems
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Problem 7
Calculate: $$0.6 \times 0.7$$
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Answer: 0.42
$$6 \times 7 = 42$$. Total 2 decimal places -> 0.42.
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Problem 8
Calculate: $$3.12 \times 1.5$$
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Answer: 4.68
$$312 \times 15 = 4680$$. Total 3 decimal places -> 4.68.
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Problem 9
Calculate: $$0.04 \times 0.25$$
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Answer: 0.01
$$4 \times 25 = 100$$. Total 4 decimal places -> $$0.0100 = 0.01$$
Division involving decimal points
$$a.b \div c.d$$
Move the decimal point in the divisor to the right to make it a whole number, move the decimal point in the dividend by the same number of places, and divide vertically.
Example
Calculate: $$14.4 \div 1.2$$
Show solution
1) Shift 1 place right: $$144 \div 12$$.
2) Result = 12.
Practice problems
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Problem 10
Calculate: $$4.8 \div 0.6$$
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Answer: 8
Shift 1 place: $$48 \div 6 = 8$$
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Problem 11
Calculate: $$1.44 \div 0.12$$
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Answer: 12
Shift 2 places: $$144 \div 12 = 12$$
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Problem 12
Calculate: $$7.5 \div 0.25$$
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Answer: 30
Shift 2 places: $$750 \div 25 = 30$$
Always line up decimal points vertically! Pad with trailing zeros if needed.