Problems about parts of a whole
Problems about parts of a whole in Grade 7 use the relationship part + part = whole (a + b = w), where knowing any two values lets you find the third. In Saxon Math, Course 2, students apply this to fractions, percents, and real-world problems. For example, if 2/5 of students went to the museum, then 5/5 - 2/5 = 3/5 did not go. If a battery is 82% charged, it is 18% not charged. This additive pattern is foundational for all fraction and percent problem types and connects to equation solving across Grade 7 math.
Key Concepts
Property Problems about parts of a whole have an addition thought pattern. $$ \text{part} + \text{part} = \text{whole} $$ $$ a + b = w $$.
Examples If $\frac{2}{5}$ of students went to the museum, the fraction who did not go is $\frac{5}{5} \frac{2}{5} = \frac{3}{5}$. If a phone battery is 82% charged, the percent that is not charged is $100\% 82\% = 18\%$. If a team won 9 out of 15 games, the part they did not win is $15 9 = 6$ games.
Explanation Think of a whole pie! If you know the size of one slice, you can figure out what's left. Just subtract the part you know from the whole (which is 1 or 100%) to find the unknown part. Easy as pie!
Common Questions
What does part + part = whole mean in Grade 7 math?
The whole equals the sum of its parts. If you know the whole and one part, subtract to find the other part. The equation is a + b = w, so b = w - a.
How do you use the parts-of-a-whole model with fractions?
If 2/5 of a group has a certain property, the remaining fraction is 5/5 - 2/5 = 3/5. The whole (5/5 = 1) minus one part gives the other part.
How does this apply to percent problems?
If 82% of a battery is charged, then 100% - 82% = 18% is not charged. The whole is always 100%.
Where are problems about parts of a whole taught in Saxon Math Course 2?
This concept is introduced in Saxon Math, Course 2, as a foundational problem-solving pattern for Grade 7.
How does part + part = whole connect to equation solving?
It directly models a + b = w, a linear equation. Given any two values, you isolate the third using subtraction — the same strategy used for all one-step equations.
What real-life situations use parts of a whole?
Splitting a budget, finding the remaining distance in a trip, calculating the unshaded area on a shape, and determining the unpaid balance on a bill all use part + part = whole.
What mistake do students make with parts-of-a-whole problems?
Students sometimes add the given part to the whole (doubling it) instead of subtracting to find the missing part.