Problems about combining
Problems about combining involve adding two or more quantities to find a total. These may include whole numbers, fractions, decimals, or mixed measures. The key is identifying all the parts to be combined, choosing the correct addition method (finding common denominators for fractions, aligning decimal points, or converting units for mixed measures), and computing the sum. This 7th grade skill from Saxon Math Course 2 is one of the most fundamental problem types — combining quantities appears in every area of math and daily life.
Key Concepts
Property some + some more = total $s + m = t$.
Examples A troop of 175 scouts is joined by 137 more. The total is $175 + 137 = 312$ scouts. You need 114 miles for a trip and have gone 47. You still need $114 47 = 67$ miles.
Explanation Think of this as joining groups! You start with some items, add more, and find the new total. If you know the total but not one of the starting parts, you can work backward by subtracting.
Common Questions
What are combining problems in math?
Combining problems ask you to add two or more quantities to find a total. They are recognized by words like "altogether," "total," "in all," "combined," and "sum."
How do you solve a combining problem with fractions?
Find a common denominator, convert both fractions, then add the numerators. For 1/3 + 1/4: LCD = 12, so 4/12 + 3/12 = 7/12.
How do you solve a combining problem with decimals?
Align the decimal points, add zeros if needed to make them the same length, then add as whole numbers. For 3.4 + 1.25: align and add to get 4.65.
What grade covers combining problems?
Combining problems run throughout all grades. In 7th grade Saxon Math Course 2, they appear with more complex numbers including fractions, decimals, mixed measures, and signed numbers.
What are key words that signal a combining problem?
Words and phrases like "total," "sum," "in all," "altogether," "combined," and "both" signal that you should add the quantities given.
How is a combining problem different from a separating problem?
Combining adds quantities together to find a total. Separating (take-away or comparison) subtracts one quantity from another. Recognizing the difference is the first step in selecting the right operation.