Operations with Decimals: Additional Practice (Set 1)

Subtract to find the missing addend, lining up the points.

$5.05 - 1.45 = 3.60$

So $3.\square = 3.6$, which means the blank is $6$. Checking, $3.60 + 1.45 = 5.05$.

The divisor $0.004$ has three decimal places, so slide both points three places to the right. The divisor becomes $4$ and the dividend becomes $2500$ (two trailing zeros fill the extra slides).

$2.5 \div 0.004 = 2500 \div 4 = 625$

The number of cups is the total volume divided by the volume of one cup. Slide both points two places right so the divisor is whole.

$1.5 \div 0.25 = 150 \div 25 = 6$

So $6$ full cups can be poured.

Multiply two factors first, then the third, counting places each time.

$0.7 \times 0.8 = 0.56$

Then multiply by the last factor.

$0.56 \times 0.5 = 0.28$

Two places times one place gives three places, but the trailing zero in $0.280$ is dropped.

The divisor $0.9$ has one decimal place, so slide both points one place to the right. The divisor becomes $9$ and the dividend becomes $0.45$.

$0.045 \div 0.9 = 0.45 \div 9 = 0.05$

Nine goes into $45$ hundredths five times, giving five hundredths.

Do the subtraction inside the parentheses first, lining up the points.

$3.2 - 1.7 = 1.5$

Then multiply, counting decimal places: $15 \times 6 = 90$ with $1 + 1 = 2$ places.

$1.5 \times 0.6 = 0.90 = 0.9$

Distance is speed times time, so multiply $0.85$ by $6$. As whole numbers, $85 \times 6 = 510$, and the product keeps two decimal places.

$0.85 \times 6 = 5.10 = 5.1$

The car travels $5.1$ km.

Evaluate each. The first multiplies as whole numbers ($2 \times 3 = 6$) with $1 + 1 = 2$ decimal places.

$0.2 \times 0.3 = 0.06$

The others do not match: $0.2 + 0.3 = 0.5$, then $0.6 \div 0.1 = 6 \div 1 = 6$, and $0.6 \times 0.5 = 0.30 = 0.3$. Only $0.2 \times 0.3$ equals $0.06$.

By the order of operations, multiply before subtracting. First the product: $4 \times 5 = 20$ with one decimal place.

$0.4 \times 5 = 2.0$

Then subtract from $7$.

$7 - 2 = 5$

The product has two decimal places, so the whole-number product is $32$. Divide by the known factor's digits: $32 \div 4 = 8$.

$0.8 \times 0.4 = 0.32$

So the blank is $8$.

The divisor $0.05$ has two decimal places, so slide both points two places to the right. The divisor becomes $5$ and the dividend becomes $1350$.

$13.5 \div 0.05 = 1350 \div 5 = 270$

First the correct product: $45 \times 2 = 90$ with $2 + 1 = 3$ decimal places, so $0.45 \times 0.2 = 0.090 = 0.09$. The student's $0.9$ is ten times too big from miscounting the places.

$\frac{0.09}{0.9} = \frac{9/100}{9/10} = \frac{10}{100} = \frac{1}{10}$

So the correct answer is one tenth of what the student wrote.