A recipe uses 1/4 teaspoon of salt and 2 1/2 teaspoons of sugar. What is the ratio of salt to sugar in this recipe?

A recipe uses 1/4 teaspoon of salt

October 20, 2026

2019 Handbook

2019 Test B Math · Question 10 of 57

Question

A recipe uses $\frac{1}{4}$ teaspoon of salt and $2\frac{1}{2}$ teaspoons of sugar. What is the ratio of salt to sugar in this recipe?

A $1:20$
B $1:10$
C $1:5$
D $1:4$

Show the answer

Correct answer: B

$\frac{1}{4} : 2\frac{1}{2}$

$\frac{1}{4} : \frac{5}{2}$

$4\left(\frac{1}{4}\right) : 4\left(\frac{5}{2}\right)$

$1 : 10$

Question analysis

A recipe calls for 1/4 teaspoon of salt and 2 1/2 teaspoons of sugar, and students write the ratio of salt to sugar in whole numbers. It tests ratios whose terms are a fraction and a mixed number. Both terms have to be rescaled together, and the mixed number is where slips creep in.

NYS standards: 7.RP.1 unit rates with fractions
6.RP.1 ratio concepts and language
Grade level: Grade 7 content, by NYS standard
Compared with grade 7: At grade 7 Ratios of fractions are grade 7 content, and this one is routine: convert a single mixed number, then scale both terms up to whole numbers. It asks for no further use of the ratio.
Estimated difficulty: Straightforward: two steps or one careful reading.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: Error-prone arithmetic moderate
An answer in an unexpected form minor
Solution: 2 steps
Reading level: Question and choices: about grade 6, 27 words.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

A ratio of a fraction to a mixed number is unfamiliar enough that students reach for shortcuts, and each shortcut has a choice waiting. Pairing numerators after converting, or reading the salt's 1/4 as a ratio by itself, never compares the two amounts properly. Scaling both terms by the same factor, 4, or asking how many quarter teaspoons fit into 2 1/2 teaspoons, keeps the comparison intact.

Error-prone arithmetic moderate Working it out
The sugar is a mixed number, so 2 1/2 must become 5/2, and both terms must then be multiplied by 4, or 5/2 divided by 1/4, without dropping a denominator. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
An answer in an unexpected form minor Choosing the answer
The recipe gives a fraction and a mixed number, but every choice is a whole-number ratio, so 1/4 : 2 1/2 has to be recognized in its scaled form. (Enright, Morley & Sheehan, 2002)

Strategy: Change 2 1/2 to 5/2, then divide the salt amount by the sugar amount; the quotient, written as a fraction with numerator 1, gives the ratio directly.

Traps

A faulty procedure: A systematic but wrong procedure: adding fractions straight across, applying an exponent to each term of a sum, dropping a sign when moving a term.
Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.
An arithmetic slip: The right method with a plausible arithmetic error: a digit, a place value or a times-table fact.

The wrong answers, classified

A An arithmetic slip (Junker & Sijtsma, 2001)
Reveals a slip Expected pull: weak
Multiplies both terms by 4 but takes 4 × 5/2 as 20, multiplying the numerator and forgetting to divide by the 2.
C A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Reveals a misconception Expected pull: strong
Rewrites 2 1/2 as 5/2 and pairs the numerators, 1 : 5, as if 1/4 and 5/2 shared a denominator.
D Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: moderate
Reads the 1/4 teaspoon of salt as the ratio 1 : 4 itself, never bringing the 2 1/2 teaspoons of sugar into the comparison.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Changing a mixed number to a fraction: $2\frac{1}{2} = \frac{2 \times 2 + 1}{2}$; A mixed number is a whole number plus a fraction. Multiply the whole number by the bottom number to count the halves in the wholes. Then add the top number, and keep the same bottom. Two wholes are 4 halves, so 2 and a half is 5 halves.
Equivalent ratios: $a : b = (a \times k) : (b \times k)$; a and b are the two amounts in a ratio, in order. k is any number except 0. Multiplying both amounts by the same number keeps the comparison the same. Use it to turn the fractions in a ratio into whole numbers.

Sort out the question
The recipe uses $\frac{1}{4}$ teaspoon of salt and $2\frac{1}{2}$ teaspoons of sugar. A ratio compares two amounts. “Salt to sugar” means salt first, then sugar. Every choice is a ratio of whole numbers. So you need to turn the two amounts into whole numbers that compare the same way.
Change the mixed number to a fraction
A mixed number is hard to work with. Write the sugar as a fraction.
$2\frac{1}{2} = \frac{2 \times 2 + 1}{2}$
$2\frac{1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$
So the ratio of salt to sugar is $\frac{1}{4} : \frac{5}{2}$ .
Multiply both parts by 4
Multiply both parts by the same number to clear the fractions. Use 4, because both bottom numbers, 4 and 2, go into 4.
$a : b = (a \times k) : (b \times k)$
$\frac{1}{4} : \frac{5}{2} = \left(\frac{1}{4} \times 4\right) : \left(\frac{5}{2} \times 4\right) = 1 : 10$
For the sugar, $5 \times 4 = 20$ , and then $20 \div 2 = 10$ .
Watch out: forgetting to divide by 2 gives 1 : 20, choice A. Pairing the top numbers, 1 : 5, choice C, compares quarters with halves. And 1 : 4, choice D, is only the salt amount. It leaves out the sugar.
So the answer is B, 1 : 10.

Check your answer

Think in quarter teaspoons. The salt is 1 quarter teaspoon. One teaspoon is 4 quarters, so the sugar is $2.5 \times 4 = 10$ quarter teaspoons. That is 1 quarter of salt for every 10 quarters of sugar, or 1 : 10.

The original DOE question

Question 67 as printed on page 178 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2019–2020, page 178, question 67. Open page 178 of the handbook (PDF)