What is the first step to estimate the difference between two numbers?
Just like with sums, the first step is to round each number to the same place value (like the nearest ten or hundred).
Estimate the difference by rounding each number to the nearest ten: \(82 - 49\)
Round \(82\) to \(80\). Round \(49\) to \(50\). The estimated difference is \(80 - 50 = 30\).
Estimate the difference by rounding each number to the nearest ten: \(67 - 21\)
Round \(67\) to \(70\). Round \(21\) to \(20\). The estimated difference is \(70 - 20 = 50\).
When you estimate a difference, do you subtract first or round first?
You must round the numbers FIRST, and then subtract the rounded numbers.
Estimate the difference by rounding each number to the nearest hundred: \(789 - 312\)
Round \(789\) to \(800\). Round \(312\) to \(300\). The estimated difference is \(800 - 300 = 500\).
Estimate the difference by rounding each number to the nearest hundred: \(905 - 451\)
Round \(905\) to \(900\). Round \(451\) to \(500\). The estimated difference is \(900 - 500 = 400\).
Juan had \(91\) trading cards and gave \(28\) away. About how many cards does he have left?
Round \(91\) to \(90\) and \(28\) to \(30\). Juan has about \(90 - 30 = 60\) cards left.
A bike costs \(242\). You have saved \(119\). About how much more money do you need?
Round \(242\) to \(200\) and \(119\) to \(100\). You need about \(200 - 100 = 100\) more. Or, for a closer estimate, round to the tens: \(240 - 120 = 120\).
Estimate the difference: \(94 - 55\)
Round \(94\) to \(90\). Round \(55\) to \(60\). The estimated difference is \(90 - 60 = 30\).
Estimate the difference: \(536 - 188\)
Round \(536\) to \(500\). Round \(188\) to \(200\). The estimated difference is \(500 - 200 = 300\).
Why is it important to round both numbers before subtracting?
Rounding both numbers makes the mental math much simpler. Subtracting first (e.g., \(789 - 312 = 477\)) and then rounding (\(500\)) is more work and defeats the purpose of estimation.
