Subtracting Mixed Measures
Subtracting mixed measures in Grade 7 requires converting units before subtracting when the smaller unit in the minuend is insufficient. In Saxon Math, Course 2, students borrow from larger units — just as in whole-number borrowing — to create enough of the smaller unit to subtract. For example, 5 days 10 hr - 2 days 15 hr requires borrowing 1 day (24 hours), giving 4 days 34 hr - 2 days 15 hr = 2 days 19 hr. This skill applies to time, length, weight, and other measurement systems with multiple units.
Key Concepts
Property When subtracting mixed measures, it is often necessary to convert units before you can subtract.
Examples To solve 5 days 10 hr 2 days 15 hr, first borrow 1 day: 4 days 34 hr 2 days 15 hr = 2 days 19 hr. To solve 4 yd 5 in. 1 yd 1 ft 8 in., first borrow 1 yard, then 1 foot: 3 yd 2 ft 17 in. 1 yd 1 ft 8 in. = 2 yd 1 ft 9 in.
Explanation Subtraction can get tricky when you need to subtract a larger number from a smaller one. The secret is to 'borrow' from the bigger unit to the left, converting it into smaller pieces (like 1 hour becomes 60 minutes). This gives you enough to subtract easily across all units.
Common Questions
How do you subtract mixed measures in Grade 7?
If the smaller unit of the minuend is less than the smaller unit of the subtrahend, borrow from the next larger unit, convert it to the smaller unit, and add it before subtracting.
Can you show an example of subtracting mixed measures with time?
5 days 10 hr - 2 days 15 hr: borrow 1 day (24 hr) → 4 days 34 hr - 2 days 15 hr = 2 days 19 hr.
How do you subtract mixed measures with yards, feet, and inches?
Convert as needed: 1 yard = 3 feet, 1 foot = 12 inches. Borrow from yards to get feet, and from feet to get inches before subtracting.
Why do you sometimes need to borrow twice when subtracting mixed measures?
When the problem involves three units (like yards, feet, inches), you may need to first borrow a yard to get more feet, then borrow a foot to get more inches.
Where is subtracting mixed measures covered in Saxon Math Course 2?
This skill is taught in Saxon Math, Course 2, as part of Grade 7 measurement and conversion operations.
Is this like borrowing in regular subtraction?
Yes. The concept is the same — when the bottom digit is larger than the top digit, you borrow from the next place value and convert. The difference is that the conversion factor varies by measurement unit.
What common mistakes occur when subtracting mixed measures?
Students often forget the conversion rate between units (thinking 1 foot = 10 inches instead of 12), borrow the wrong amount, or forget to reduce the larger unit after borrowing.