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Estimating Calculations
Select the skills to practice, and then click Go!
Foundational skills
Write the estimation calculation
\[ 4.82 \times 19.3 \rightarrow 5 \times 20 \]
Write down a calculation using rounded values that could be used to estimate an answer.
Estimating single operations
Estimate an addition
\[ 5.82 + 3.14 \]
Round each number to 1 significant figure and add them to find an estimate.
Estimate a subtraction
\[ 847 – 312 \]
Round each number to 1 significant figure and subtract to find an estimate.
Estimate a multiplication
\[ 6.2 \times 48 \]
Round each number to 1 significant figure and multiply to find an estimate.
Estimate a division (whole number divisor)
\[ 5765 \div 19.2 \]
Round each number to 1 significant figure and divide to find an estimate.
Estimate a division (decimal divisor)
\[ 3.72 \div 0.48 \]
Round each number to 1 significant figure and divide when the divisor is a decimal.
Estimating multiple operations
Estimate with two operations
\[ 4.1 \times 19 + 32 \]
Round each number and perform two operations to find an estimate.
Estimate with brackets
\[ (7.2 + 4.8) \times 2.9 \]
Round each number and use brackets to find an estimate.
Estimate with three or more operations
\[ \frac{6.1 \times 38}{1.92} \]
Round each number and perform multiple operations to find an estimate.
Determining over or underestimate
Over or underestimate: addition
\[ 482 + 317 \approx 500 + 300 \]
Work out whether an estimated sum is larger or smaller than the actual answer.
Over or underestimate: subtraction
\[ 847 – 312 \approx 800 – 300 \]
Work out whether an estimated difference is larger or smaller than the actual answer.
Over or underestimate: multiplication
\[ 6.2 \times 48 \approx 6 \times 50 \]
Work out whether an estimated product is larger or smaller than the actual answer.
Over or underestimate: division
\[ 847 \div 19.2 \approx 800 \div 20 \]
Work out whether an estimated quotient is larger or smaller than the actual answer.
Over or underestimate: combined
\[ \frac{6.1 \times 38}{1.9} \]
Work out whether an estimate involving multiple operations is larger or smaller than the actual answer.
Checking and improving estimates
Check if an answer is reasonable
\[ 5.1 \times 38 = 1938 \text{ ?} \]
Use estimation to check whether a given answer to a calculation is reasonable.
Improve an estimate
\[ 4.9 \times 21 \approx \text{ ?} \]
Find a closer estimate by choosing different rounded values.
Problems in context
Estimate in context: single operation
\[ \text{£}18.75 \times 41 \]
Use estimation to answer a problem set in a real-life context with one operation.
Estimate in context: multiple operations
\[ 3 \times \text{£}8.95 + \text{£}25 \]
Use estimation to answer a problem requiring multiple operations.
Special cases
Estimate with very large numbers
\[ 4{,}720{,}000 \times 5.8 \]
Estimate calculations involving very large numbers.
Estimate with very small decimals
\[ 0.0317 \times 48 \]
Estimate calculations involving very small decimal numbers.
Timer (Optional)
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Question