Greater than and less than signs: what > and < mean and how to never mix them up

Your first grader's worksheet says 34 ☐ 43, and the two of you are staring at the box. The greater than sign and the less than sign look almost the same, and adults mix them up too. Two rules settle it for good: the open side faces the bigger number, and a greater than less than sentence is read from left to right like any other sentence.

Why the greater than and less than signs matter

The greater than and less than signs let a child write a comparison as a short math sentence. The sign > means "is greater than", so 7 > 3 reads "7 is greater than 3". The sign < means "is less than", so 2 < 9 reads "2 is less than 9", and the sign = says both sides are the same amount.

Comparing numbers starts early in US schools. Common Core standard 1.NBT.B.3 asks first graders to "compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <." Standard 2.NBT.A.4 does the same with three-digit numbers, and the guide to what math each grade should know shows where the skill sits in the year.

The signs themselves are almost 400 years old. They first appeared in print in 1631 in Thomas Harriot's book Artis Analyticae Praxis, published 10 years after his death, and the MacTutor History of Mathematics archive notes that they "were introduced by the editor" because Harriot "himself used different symbols".

The two readings: a sentence and a shape

A comparison can be read in two ways, and a child needs both. The first reading is a sentence from left to right: "7 is greater than 3." The second reading is a shape: the wide open side faces the bigger number and the narrow point faces the smaller number.

The shape reading tells a child which way to draw the sign. The sentence reading tells the child what the sign says, and it is the one that works for every pair, including fractions, decimals and negative numbers.

How to compare two numbers, step by step

Comparing two numbers is a place value job, and the sign comes last. These five steps work for whole numbers of any size.

1. Count the digits. A whole number with more digits is bigger, so 105 > 98 because 105 has three digits and 98 has two.
2. Compare the leftmost digits. When the numbers have the same number of digits, start at the biggest place. In 34 and 43, the tens digits are 3 and 4, so 34 is smaller.
3. Move right on a tie. If the leftmost digits match, compare the next place. In 562 and 527, the hundreds are both 5, and the tens are 6 and 2, so 562 is bigger.
4. Point at the smaller number. Draw the sign with its point toward the smaller number and its open side toward the bigger one: 34 < 43 and 562 > 527.
5. Read the sentence aloud. Say the whole sentence from left to right: "34 is less than 43." If the words sound wrong, the sign is backwards.

Play free in your browserComparing NumbersK–Grade 1

The free comparing numbers game runs this exact routine in the browser with no sign-up. If step 2 is shaky, the guide to place value for parents explains tens and ones with the same kitchen-table objects.

The part people get wrong: decimals and negative numbers

Decimals break the "more digits means bigger" rule. In 0.5 and 0.45, the number 0.45 has more digits, but 0.5 is bigger: write it as 0.50, compare 50 hundredths with 45 hundredths, and you get 0.5 > 0.45. Common Core 5.NBT.A.3b asks fifth graders to "compare two decimals to thousandths based on meanings of the digits in each place", and the guide to decimals for parents covers the zeros trick.

Negative numbers flip a child's instinct. The number 7 is bigger than 3, but −7 is smaller than −3, because −7 is further below zero: −3 > −7. The guide to negative numbers shows why with a thermometer, since −3 °F is warmer than −7 °F.

Memory tricks for greater than and less than, side by side

Four memory tricks are common, and each one suits a different age. The best choice is the one that still works when the numbers get harder.

Which trick to pick

The point-to-the-smaller rule is the trick to keep. The alligator is a good start for a five-year-old, but older children should hear "the open side faces the bigger number" because it is the same rule without the story. The number line takes over once negative numbers and decimals arrive.

Practice greater than and less than at home

Greater than and less than practice works best with real objects first and digits second. Five minutes a day with cards, dice or prices builds the habit faster than one long worksheet.

• Two piles of buttons: make two piles, count each, then lay two craft sticks between them as a sign with the open side toward the bigger pile.
• Card flip: each player flips a playing card, and the player who reads the sentence correctly ("9 is greater than 4") keeps both cards.
• Dice tens and ones: roll two dice to make a two-digit number, roll again for a second number, then compare them. This is 1.NBT.B.3 at the kitchen table.
• Price check: at the store, compare two prices, such as $3.49 and $3.94, and say which item costs less.

A number line ties the tricks together. OpenStax Prealgebra 2e states that "going from left to right, numbers increase in value", so the bigger of any two numbers sits further right. Common Core 6.NS.C.7a asks sixth graders to "interpret −3 > −7 as a statement that −3 is located to the right of −7 on a number line".

The practice rule: read the sentence aloud

The read-aloud rule fixes most backwards signs. After your child writes a comparison, ask them to read it from left to right with the words "is greater than" or "is less than". A child who writes 6 > 9 and reads "6 is greater than 9" usually hears the problem at once.

Keep the order of the numbers fixed in practice. Write the two numbers first, then ask for the sign, so the child chooses the sign and never swaps the numbers to fit a favorite sign. For first-grade games that build the same number sense, see the math games for 1st graders.

How to measure progress with comparing numbers

Five short checks show whether your child understands the signs or is guessing. Ask them on different days, without hints, and note which ones need a second try.

• Two-digit numbers: fill the box in 47 ☐ 74. The answer is 47 < 74.
• Three-digit numbers: fill the box in 309 ☐ 290. The answer is 309 > 290, because 3 hundreds beat 2 hundreds.
• Equal values: fill the box in 5 + 3 ☐ 8. The answer is =, because both sides are 8.
• Read it back: read 61 > 16 aloud. The answer is "61 is greater than 16".
• Flip it: write 61 > 16 the other way round. The answer is 16 < 61.

Play free in your browserPlace ValueGrade 1–2

A workable test: ten pairs in two minutes

A two-minute test with ten pairs gives a clear number to track. Write ten pairs of two-digit numbers, mix in two pairs with the same tens digit, such as 52 and 58, and count correct signs. Nine or ten correct with every sentence read aloud means the skill is secure, and you can move to three-digit numbers.

Common mistakes with greater than and less than

Four mistakes cause most wrong comparisons, and each has a short fix.

• Backwards sign: the child writes 3 > 8 because the alligator "faces" the wrong way. Ask for the sentence aloud and point at the open side.
• Comparing the last digit: the child says 29 > 41 because 9 is more than 1. Cover the ones digits and compare the tens first.
• Longer decimal wins: the child says 0.45 > 0.5. Add a zero so both have the same number of decimal places, then compare 45 and 50.
• Bigger digit, bigger negative: the child says −7 > −3. Draw a number line and ask which number is further right.

Edge case: ≥, ≤ and ≠, and how to type them

Three more signs build on the same shapes. The sign ≥ means "greater than or equal to", ≤ means "less than or equal to", and ≠ means "is not equal to", so x ≥ 5 includes 5 itself while x > 5 does not. These signs show up in middle school inequalities and in spreadsheets.

Typing the signs is easier than it looks. On a US keyboard, > is Shift and the period key, and < is Shift and the comma key. A Mac types ≥ with Option and period and ≤ with Option and comma; spreadsheets and most code accept >= and <=.

Your greater than and less than checklist and next steps

• Open side: the open side faces the bigger number and the point faces the smaller one.
• Read it: read every comparison aloud from left to right.
• Place value: count digits, then compare from the leftmost place.
• Decimals: add zeros so both decimals have the same number of places.
• Negatives: the number further right on the number line is bigger.
• Equal: use = when both sides have the same value.

Once whole numbers are secure, comparing fractions uses the same signs with one extra step: find a common denominator first.

MathIt is a free app for iOS and Android with about 90 game types and adaptive difficulty, so a child who compares two-digit numbers today meets three-digit numbers when they are ready.