Number Concepts and Operations: Fractions, Decimals and Percents
Fractions as partitioned bars, decimals, percent as a hundred-square filling, plus negative numbers and absolute value as distance from zero.
11 topics · 49 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Fractions as Parts of a Whole
- How it worksHow does the bottom number of a fraction say how many equal parts the bar was cut into?
- How it worksHow can one fraction be a piece of a bar, a point on a number line, and a division problem at once?
- Worked exampleShow me 3/4 as a shaded bar, as a point on a number line, and as 3 divided by 4.
- Common mistakeWhy isn't 1/3 of a large pizza the same amount of food as 1/3 of a small one?
Your turneasy1 of 3
A candy bar is cut into 10 equal pieces and you take 2 of them. What fraction of the bar do you have, written as a decimal? Round to two decimal places.Equivalent Fractions and Lowest Terms
- How it worksHow does slicing every piece of a bar into three smaller pieces leave the shaded part unchanged?
- Worked exampleFind 42/56 in lowest terms by pulling out the greatest common factor.
- Common mistakeWhy doesn't adding 1 to the top and 1 to the bottom of 2/3 produce an equal fraction?
Your turnhard1 of 3
The fraction 7/8 is rewritten with a bottom number of 8 times 6. What is the new top number?Comparing and Ordering Fractions
- How it worksHow does a common denominator line two fractions up on one ruler so you can see which is longer?
- How it worksHow does cross multiplying settle which of two fractions is larger in a single step?
- Worked exampleFind the order of 2/3, 5/8 and 7/12 from smallest to largest.
- Worked exampleFind which is larger, 7/9 or 8/11, by measuring how far each one sits below 1.
- Common mistakeWhy isn't the fraction with the bigger bottom number always the smaller fraction?
Your turnmedium1 of 3
How far below 1 does the fraction 8/13 sit? Give your answer as a decimal to three places.Adding and Subtracting Fractions
- How it worksHow does a common denominator re-cut both bars so the pieces finally match in size?
- Worked exampleFind 3/4 plus 5/6 and write the answer as a mixed number.
- Worked exampleFind 5 and 1/3 minus 2 and 3/4 by borrowing from the whole number.
Your turneasy1 of 3
Find 3/4 plus 5/6. Give your answer as a decimal to three places.Multiplying and Dividing Fractions
- How it worksHow does multiplying two fractions show up as a rectangle drawn inside another rectangle?
- How it worksHow does flipping the second fraction turn a division problem into a multiplication problem?
- Worked exampleFind 2/3 times 9/10 by cancelling common factors before you multiply.
- Worked exampleFind 3/4 divided by 2/5 and explain what the answer is actually counting.
- Common mistakeWhy doesn't dividing by a fraction always hand you a bigger answer than you started with?
Your turneasy1 of 3
Find 2/3 times 11/10 by cancelling before you multiply. Give your answer as a decimal to three places.Decimals and Decimal Arithmetic
- How it worksHow does lining up the points keep tenths with tenths and hundredths with hundredths?
- How it worksHow do you count decimal places to park the point correctly in 0.3 times 0.04?
- Worked exampleFind 0.25 times 0.4 and show why the answer needs three decimal places before trimming.
- Worked exampleFind 7.2 divided by 0.09 by sliding both decimal points two places to the right.
- Going furtherWhat happens to a decimal when you multiply it by 10, then 100, then 1000 in a row?
Your turneasy1 of 3
Find 0.25 times 0.7, writing the answer as a decimal.Converting Fractions, Decimals and Percents
- How it worksHow does dividing the top by the bottom turn any fraction into a decimal?
- How it worksHow does percent literally mean out of one hundred on a hundred-square grid?
- Worked exampleFind the decimal and the percent that match 5/8, with no calculator.
- Worked exampleFind the lowest-terms fraction for 0.36 and the lowest-terms fraction for 12 percent.
- Common mistakeWhy isn't 0.5 percent the same amount as 0.5 on a hundred-square grid?
Your turnmedium1 of 3
Write 5/8 as a percent, with no calculator.Percent of a Number and Finding the Whole
- How it worksHow does a hundred-square filling up show exactly what 30 percent of a quantity means?
- How it worksHow do you run a percent problem backwards from a part to the whole it came from?
- Worked exampleFind 15 percent of 60 by splitting it into 10 percent plus 5 percent.
- Worked exampleFind the original price when 40 percent of it comes to 18 dollars.
Your turneasy1 of 3
Find 15 percent of 151 by taking 10 percent and then half of that again.Percent Increase and Percent Decrease
- How it worksHow does a 20 percent rise become a single multiplication by 1.2 instead of two steps?
- How it worksHow does percent change compare the change to the starting amount rather than the ending one?
- Worked exampleFind the final price of a 50 dollar shirt after a 20 percent rise and then a 20 percent cut.
- Worked exampleFind the percent increase when a class grows from 24 students to 30 students.
- Common mistakeWhy isn't a 30 percent discount followed by a 20 percent discount the same as 50 percent off?
Your turnmedium1 of 3
A shirt costs 74 dollars. Its price rises 20 percent and then falls 20 percent. What is the final price? Round to two decimal places.Negative Numbers on the Number Line
- How it worksHow does adding a negative number walk you left along the number line instead of right?
- How it worksHow does subtracting a negative become adding, drawn as reversing direction twice?
- Worked exampleFind negative 7 plus 12 minus negative 4 by walking the steps out on a number line.
- Worked exampleFind the distance between negative 6 and 9 on the number line.
- Common mistakeWhy isn't negative 10 greater than negative 3 even though 10 is greater than 3?
Your turneasy1 of 3
Find negative 7 plus 18 minus negative 7.Absolute Value as Distance from Zero
- How it worksHow does absolute value measure distance from zero while ignoring which side you stand on?
- Worked exampleFind the absolute value of negative 12 minus the absolute value of 5.
- Worked exampleFind both numbers whose distance from zero is 6, and show them as a matching pair.
- Common mistakeWhy doesn't absolute value just mean crossing off the minus sign in front of an expression?
- Going furtherWhat happens to the absolute value of a number as it slides from negative 5 up through zero to 5?
Your turneasy1 of 3
Find the absolute value of negative 19 minus the absolute value of 7.AP®, SAT® and PSAT/NMSQT® are trademarks registered by the College Board (PSAT/NMSQT® jointly with the National Merit Scholarship Corporation). ACT® is a registered trademark of ACT Education Corp. GRE® is a registered trademark of ETS. LSAT® is a registered trademark of the Law School Admission Council. MCAT® is a registered trademark of the Association of American Medical Colleges. ISEE® and SSAT® are registered trademarks of their owners. None of these organizations is affiliated with, or endorses, Jentoo.