Math Foundations
Strengthen number sense, fractions, ratios, expressions, equations, geometry, and data—the bridge from middle-school math to high-school success.
- Problem types
- 634
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Page 4 of 18
Each problem type has four distinct practice variants. Open a preview to move among all four.
Order rational numbers across forms
Compare and order rational numbers written as fractions, decimals, and percents.
Ordering mixed forms is safest after converting everything to one representation. We’ll write the percent and fraction as decimals, align all values through the thousandths place, and compare from left …
Preview problemChoose the best benchmark match
Compare and order rational numbers written as fractions, decimals, and percents.
Closeness to one half means the smallest absolute distance from the benchmark, not merely a familiar-looking form. We’ll rewrite one half and every candidate on a common decimal scale, calculate …
Preview problemComplete a rational-number comparison
Compare and order rational numbers written as fractions, decimals, and percents.
The missing fraction must satisfy two strict comparisons, so values equal to either endpoint do not count. We’ll rewrite zero point six and seventy percent on one decimal scale and …
Preview problemCompare contextual rational quantities
Compare and order rational numbers written as fractions, decimals, and percents.
Because the stores discount the same kind of backpack, comparing their rates is enough to compare the amount saved. We’ll convert the fractional discount to a percent, place all three …
Preview problemFind the closest contextual benchmark match
Compare and order rational numbers written as fractions, decimals, and percents.
Closest means the smallest distance from seventy-five percent, whether a class rate lies above or below it. We’ll convert every rate to percent form, calculate each absolute percentage-point gap from …
Preview problemClassify rational numbers by benchmark range
Compare and order rational numbers written as fractions, decimals, and percents.
We’ll use zero point five and one as the two benchmark boundaries and rewrite every mixed-form value as a decimal. Each value then gets tested against both boundaries before it …
Preview problemCheck a mixed-form ordering claim
Compare and order rational numbers written as fractions, decimals, and percents.
To judge the student’s ordering claim, we’ll rebuild the order independently instead of relying on how the forms look. We’ll convert the percent and fraction to decimals, align all three …
Preview problemConvert to a common form for comparison
Compare and order rational numbers written as fractions, decimals, and percents.
This task asks for both the decimal conversions and the least-to-greatest order, so we’ll keep those stages separate. We’ll interpret tenths by place value, turn the percent into hundredths, align …
Preview problemName a benchmark in several forms and compare it
Compare and order rational numbers written as fractions, decimals, and percents.
The bar gives a part-to-whole fraction: count shaded equal sections for the numerator and all equal sections for the denominator. We’ll convert that fraction to a decimal, express the same …
Preview problemFilter a mixed-form set by benchmark conditions
Compare and order rational numbers written as fractions, decimals, and percents.
The conditions create an open interval: a value must be strictly above zero point four and strictly below fifty percent. We’ll convert the upper bound and every mixed-form entry to …
Preview problemChoose the right mixed-form comparison strategy
Compare and order rational numbers written as fractions, decimals, and percents.
A useful common form should preserve exact values and make all three numbers easy to compare. We’ll examine which representation handles the fraction, decimal, and percent exactly and efficiently, then …
Preview problemConvert a fraction to decimal and percent
Convert among fractions, decimals, and percents and choose the most useful form for a task.
A fraction names a division, so the decimal comes from dividing the numerator by the denominator rather than combining their digits. We’ll then rewrite that decimal in hundredths and read …
Preview problemConvert a decimal to fraction and percent
Convert among fractions, decimals, and percents and choose the most useful form for a task.
The last digit in zero point three seven five is in the thousandths place, which gives a natural fraction before simplification. We’ll write that place-value fraction, divide numerator and denominator …
Preview problemConvert a percent to decimal and fraction
Convert among fractions, decimals, and percents and choose the most useful form for a task.
Percent means per hundred, so converting sixty-two point five percent to a decimal requires dividing by one hundred. We’ll express the resulting decimal as a place-value fraction, reduce it by …
Preview problemChoose the most useful rational-number form
Convert among fractions, decimals, and percents and choose the most useful form for a task.
The store-sign context tells us the useful target form is a percent, while one fourth describes the portion removed from the price. We’ll scale the fraction to an equivalent amount …
Preview problemWrite a contextual share in three forms
Convert among fractions, decimals, and percents and choose the most useful form for a task.
Maya’s completed share begins as completed questions over total questions, so the part and whole must stay in that order. We’ll simplify the fraction, divide to get the decimal, and …
Preview problemPick the best form for a context
Convert among fractions, decimals, and percents and choose the most useful form for a task.
A public weather card communicates rain chance in percent form, so the decimal must be renamed without changing its value. We’ll write zero point three using hundredths, interpret that amount …
Preview problemComplete a contextual equivalence table
Convert among fractions, decimals, and percents and choose the most useful form for a task.
Each battery row has one supplied anchor, and all three forms in that row must name exactly the same level. We’ll complete one device at a time by converting among …
Preview problemTranslate a visual model into three forms
Convert among fractions, decimals, and percents and choose the most useful form for a task.
Because the grid contains one hundred equal cells, the shaded count immediately gives both a fraction in hundredths and a percent. We’ll count the full shaded rows plus the extra …
Preview problemTranslate verbal share language into useful forms
Convert among fractions, decimals, and percents and choose the most useful form for a task.
The phrase three out of eight identifies part over whole, and the strip confirms that same relationship. We’ll check whether the fraction is already simplified, divide numerator by denominator for …
Preview problemFilter a mixed-form set for equivalence
Convert among fractions, decimals, and percents and choose the most useful form for a task.
Exact equivalence means every retained value must equal zero point six, not merely look close or contain the same digit. We’ll convert each fraction and percent to a decimal, recognize …
Preview problemChoose a smart conversion strategy
Convert among fractions, decimals, and percents and choose the most useful form for a task.
The spreadsheet requires decimals, so that target form should guide both the conversions and the final sort. We’ll divide the fraction, divide the percent by one hundred, preserve the given …
Preview problemFind a benchmark percent of a quantity
Find a percent of a quantity and interpret the result in context.
Twenty-five percent is a benchmark percent, so it can be replaced with a familiar fraction of the whole. We’ll simplify twenty-five out of one hundred, use that fraction to divide …
Preview problemFind a non-benchmark percent of a quantity
Find a percent of a quantity and interpret the result in context.
Finding thirty-five percent of a whole means multiplying the whole by thirty-five hundredths, not by the whole number thirty-five. We’ll convert the percent to a decimal and multiply by two …
Preview problemFind a percent of a decimal or rational quantity
Find a percent of a quantity and interpret the result in context.
The word of signals multiplication even when the whole is a decimal quantity. We’ll convert fifteen percent to its decimal multiplier, multiply by all of eight point four, and track …
Preview problemComplete a percent-of-quantity structure
Find a percent of a quantity and interpret the result in context.
The diagram identifies eighteen percent as the rate, two hundred fifty as the whole, and the blank as the missing part. We’ll convert the percent to a decimal, multiply it …
Preview problemFind and interpret a contextual percent amount
Find a percent of a quantity and interpret the result in context.
The whole is the forty-five students in the grade, and the percent describes the part who ride the bus. We’ll rewrite twenty percent as either a decimal multiplier or a …
Preview problemCompare percent amounts across contexts
Find a percent of a quantity and interpret the result in context.
The written percentages apply to different page totals, so comparing thirty percent with twenty percent alone cannot settle the question. We’ll compute each percent amount within its own table row, …
Preview problemUse a percent amount inside a context
Find a percent of a quantity and interpret the result in context.
The sixty percent describes filled seats, but the question asks for the complementary group of open seats. We’ll first calculate the filled part of the fifty-seat whole, subtract that part …
Preview problemCheck reasonableness in a percent-of-quantity problem
Find a percent of a quantity and interpret the result in context.
Before calculating, we’ll test the claim against a key benchmark: a positive percent below one hundred percent should produce less than the positive whole. Then we’ll convert twelve percent to …
Preview problemTranslate percent of into multiplication
Find a percent of a quantity and interpret the result in context.
The phrase thirty-five percent of eighty tickets has a standard structure: convert the percent to a decimal and replace of with multiplication. We’ll build that expression, evaluate it, and preserve …
Preview problemRead a percent model and find the part
Find a percent of a quantity and interpret the result in context.
The full bar represents one hundred fifty items, while four of its ten equal sections are shaded. We’ll find the value of one ten-percent section, scale that amount to the …
Preview problemScreen for correct percent-of-quantity representations
Find a percent of a quantity and interpret the result in context.
Every valid representation must preserve all three roles: forty percent as the rate, sixty as the whole, and the resulting part. We’ll establish that target relationship, test each equation or …
Preview problemChoose a smart percent-of-quantity strategy
Find a percent of a quantity and interpret the result in context.
The task requires the benchmark-percent strategy, so fifteen percent should be split into ten percent and five percent of the same whole. We’ll find one tenth of eighty, halve that …
Preview problemFind a percent increase
Calculate percent increase and decrease and explain what the percent measures.
Percent increase compares how much the quantity grew with where it started, so forty—not fifty—is the base. We’ll subtract the original from the new amount, divide that increase by the …
Preview problemFind a percent decrease
Calculate percent increase and decrease and explain what the percent measures.
Percent decrease measures the amount lost relative to the original eighty, not relative to the ending value. We’ll subtract the new amount from the original, divide that loss by eighty, …
Preview problem