Tips and Techniques: Finding 100% of a Number

Given a percentage of a number, how do you find 100%? We’ll show you different ways to find 100%.  

First, remember that 100% means “all of it… the whole thing.”

Example 1: 25% of what number is 5?

This question asks, “If 25% of a number is 5, then what is 100% of the number (the whole thing)?”

The strategy here is to see how many times the “percent number” (in this case, 25) goes into 100, and then count by that number until we reach 100—the whole thing.

Here, we’re told that 25% of a number is 5. So, to find 100% of the number, we count by 25s up to 100: 25, 50, 75, 100.

25% is 5, so

            50% is 10,

                        75% is 15, and

                                    100% is 20.

Example 2: A man spent $10.00, which was 20% of his money. How much money did he have to start?

If 20% of his money is $10.00, then 40% is $20.00. (20% + 20% = 40%)

Similarly, 60% is $30.00 (40% + 20% = 60%), 80% is $40.00, so 100% is $50.00—the amount of money the man had to start.

Here’s an even faster way to approach this problem. There are 5 20%s in 100%, so this problem calls for five sets of $10.00, which equals $50.00.

Example 3: 10 kids—5% of the kids enrolled at a particular school—are out sick. How many kids are enrolled at the school?

Here, 5% is 10 kids. Since there are 20 5s in 100, we multiply 20 by 10 and get 200, the total number of students at the school.

Try these:

1. 10% of what number is 8?
2. 20% of what number is 4?
3. 20% of what number is 6?
4. 50% of what number is 28?
5. 5% of what number is 11?
6. 1% of what number is 2?

Numbers add up for Hooksett Mathnasium franchise owner

Math is sometimes seen as a subject students either love or hate, something they simply get or don't get.

Not necessarily so, says Mathnasium, which brought its franchise and its motto, "children don't hate math," to Hooksett earlier this year.

"A lot of students over the years come to feel like math is something that's just torture, and they kind of hide in the back of the classroom. They hope the teacher doesn't call on them," said Martha Gagnon, center director. "They might be embarrassed, frustrated, so by the time they come to us, they just hate math."

Mathnasium aims to help them get over their anxiety.

"Once they see that we can help them make sense of math, they start to overcome their frustration, and they end up wanting to come to Mathnasium," she said. "Maybe no one ever explained it to them that way, and a lot of students end up having all of their grades improving, not just math, because they have a better outlook, more confidence."

Mathnasium, a franchise tutoring center for students in grades 2-12, opened in January. The center's memberships function like those with a gym: once a member, students may come to gymnasium as often as they like, even every day. The programs are tailor-made to student needs.

Students take an oral diagnostic-test, followed by a written test based on the oral's results, which is used to create a customized learning plan for the child.

A third of the time is spent with this customized lesson plan. The other two thirds are given to something called "number sense" and working on homework.

"A lot of the students have a real hard time with their homework, and their parents don't feel comfortable helping them because they didn't learn things necessarily the same way that students are learning them now, and it ends up being a frustration in the family," Gagnon said.

Number sense is the intuitive grasp of numbers and patterns which is as innate in the mind as language. Mathnasium attempts to reintroduce that concept to students, freeing them from the frustrating mire of rote memorization.

Jillian Roster, left, and Bailey Caulfield study at Mathnasium, which recently opened in Hooksett. (COURTESY)

The center also works to instill this number sense in students who struggle with it, using exercises to get children off of counting on their hands or get them to think in doubles, for instance.

"Number sense is something that comes naturally to some kids and not to others," she said. "What we do is we try to work with them on things like counting and grouping, proportional thinking so that when they get older, they're not coming up with an answer to a math problem and not even know when their answer is completely off the wall, and the earlier we can start working with them, the better."

Gagnon's background is in computers, and she once served as the youngest programmer at New Hampshire Insurance. After returning home from a three-year stay in Alaska, she began thinking about the next step, which she found after she heard a radio advertisement for Mathnasium.

"I've always loved math, and I was kind of at a crossroads, so I decided to pursue the opportunity," Gagnon said. "I went out and met with Mathnasium in Los Angeles, and I guess you could say the rest is history."

Mathnasium is open Monday through Thursday, 4 p.m. to 8 p.m., and Saturday 10 a.m. to 2 p.m. The cost varies between programs, but according to Gagnon, parents generally end up paying something in the range of $20 to $25 per hour of instruction. The center also has an SAT prep program, which is offered to regular high school members at no extra charge.

-- Brendan Clogston
New Hampshire Union Leader
Sunday, May 5, 2013

Larry and the Importance of Higher Education

Learning Objectives: PSAT Math Success

Most high school kids take the PSAT. Scoring high on it is both an indicator of good SAT performance and an opportunity to earn a National Merit Scholarship. It pays to treat the PSAT seriously. It just so happens, though, that doing well on the math portion of the PSAT may have more to do with having a good foundation in the subject than having advanced, harder-to-obtain skills.

A study performed by the Journal of Neuroscience found a positive link between basic, single-digit math calculation and success on the PSAT. An MRI scan showed that students with high activity in the left area of the brain, which focuses on simple mathematical exercises, had higher PSAT scores. Although the PSAT and SAT are designed to measure advanced high school-level skills and concepts, this study shows that doing well on the PSAT can be as simple as possessing basic math reasoning (and using a little memorization).

Mathnasium offers a Numerical Fluency program which assists students of all ages who don’t have a complete grasp of computation with single-digit numbers. We define fluency as the effortless recall of number facts, for example, counting by 6s, 7s, and 8s, as well being able to effortlessly calculate “7 + 8 + 9.” Mastery of exercises like these ensure that students have the mental math skills that leads to success on the PSAT and beyond.

Mathnasium’s customized lesson plans and individualized attention make sure that dedicated students attain Numerical Fluency, paving the way for success on the PSAT and beyond.

- Larry Martinek