Year 7 Computation with positive integers: free practice test with answers

Sample computation with positive integers questions with answers

Try each one before you open the answer.

1. Place value in ancient number systems

   Write the Roman numeral $\text{MCDXCIV}$ as a Hindu-Arabic number.

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   Key idea: In Roman numerals, a smaller symbol placed before a larger one is subtracted (for example $\text{IV} = 4$); otherwise the values are added.

   1. Split the numeral into groups: $\text{M} \mid \text{CD} \mid \text{XC} \mid \text{IV}$
   2. Find each value: $\text{M} = 1000$, $\text{CD} = 500 - 100 = 400$, $\text{XC} = 100 - 10 = 90$, $\text{IV} = 5 - 1 = 4$
   3. Add: $1000 + 400 + 90 + 4 = 1494$

   Answer: $1494$

2. Place value in Hindu–Arabic numbers

   Consider the number $6\,284\,917$.

   (a) What is the value of the digit $8$?

   (b) Write the number in expanded form.

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   Key idea: Each place is worth $10$ times the place to its right: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions.

   1. (a) Reading from the right, the $8$ is in the fifth place, the ten thousands place, so its value is $8 \times 10\,000 = 80\,000$
   2. (b) Write each digit multiplied by its place value: $6 \times 1\,000\,000 + 2 \times 100\,000 + 8 \times 10\,000 + 4 \times 1000 + 9 \times 100 + 1 \times 10 + 7 \times 1$

   Answer: (a) $80\,000$ (b) $6 \times 1\,000\,000 + 2 \times 100\,000 + 8 \times 10\,000 + 4 \times 1000 + 9 \times 100 + 1 \times 10 + 7 \times 1$

3. Adding and subtracting positive integers

   Use a mental strategy to find $368 + 197$.

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   Key idea: $197$ is close to $200$, so add $200$ and then take away the extra $3$.

   1. $368 + 200 = 568$
   2. $197 = 200 - 3$, so subtract $3$: $568 - 3 = 565$

   Answer: $565$

4. Algorithms for adding and subtracting

   Use the addition algorithm to find $4786 + 3958$.

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   Key idea: Line up the place values and add from the ones column, carrying any ten to the next column.

   1. Ones: $6 + 8 = 14$, write $4$, carry $1$
   2. Tens: $8 + 5 + 1 = 14$, write $4$, carry $1$
   3. Hundreds: $7 + 9 + 1 = 17$, write $7$, carry $1$
   4. Thousands: $4 + 3 + 1 = 8$
   5. The result is $8744$

   Answer: $8744$

5. Multiplying small positive integers

   Use a mental strategy to find:

   (a) $25 \times 16$

   (b) $9 \times 48$

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   Key idea: Look for friendly numbers: $25 \times 4 = 100$, and $9 = 10 - 1$.

   1. (a) $25 \times 16 = 25 \times 4 \times 4 = 100 \times 4 = 400$
   2. (b) $9 \times 48 = 10 \times 48 - 1 \times 48 = 480 - 48 = 432$

   Answer: (a) $400$ (b) $432$

6. Multiplying large positive integers

   Use the multiplication algorithm to find $347 \times 26$.

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   Key idea: Multiply by the ones digit and the tens digit separately, then add the two partial products.

   1. $347 \times 6 = 2082$
   2. $347 \times 20 = 6940$
   3. Add: $2082 + 6940 = 9022$

   Answer: $9022$

7. Dividing positive integers

   Use short division to find $7236 \div 6$.

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   Key idea: Divide each digit from left to right, carrying any remainder to the next digit.

   1. $7 \div 6 = 1$ remainder $1$; carry $1$ to make $12$
   2. $12 \div 6 = 2$ remainder $0$
   3. $3 \div 6 = 0$ remainder $3$; carry $3$ to make $36$
   4. $36 \div 6 = 6$
   5. So $7236 \div 6 = 1206$. Check: $1206 \times 6 = 7236$ ✓

   Answer: $1206$

8. Estimating and rounding positive integers

   Round each number to the nearest ten, then estimate $63.4 + 28.7 + 41.2$.

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   Key idea: Round each number to the nearest ten first, then add the rounded values to get the estimate.

   1. $63.4$ rounded to the nearest ten is $60$.
   2. $28.7$ rounded to the nearest ten is $30$.
   3. $41.2$ rounded to the nearest ten is $40$.
   4. Estimate: $60 + 30 + 40 = 130$.

   Answer: $130$

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 7 powers and prime factors worksheet
• Year 7 expressions and the distributive law worksheet
• Year 7 rounding and estimation worksheet